Ga. 2:11-16 But when Peter was come to Antioch, I withstood him to the face, because he was to be blamed. For before that certain came from James, he did eat with the Gentiles: but when they were come, he withdrew and separated himself, fearing them which were of the circumcision. And the other Jews dissembled likewise with him; insomuch that Barnabas also was carried away with their dissimulation. But when I saw that they walked not uprightly according to the truth of the gospel, I said unto Peter before them all, If thou, being a Jew, livest after the manner of Gentiles, and not as do the Jews, why compellest thou the Gentiles to live as do the Jews? We who are Jews by nature, and not sinners of the Gentiles, Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified.
Numerous commentators, beginning with F. C. Baur in centuries past, understood this event to be the core of an ultimate division between Gentile/Pauline and Jewish/Petrine Christianity, and from there hypothesize all manner of ideas about the evolution of Christianity into a Pauline mutation of salvation by grace through a divine Christ, versus a salvation by works in which Christ was only a nice teacher and not divine. Some even call this the event that founded modern Christianity.
Let's consider this passage in more detail, and to begin, we must consider some background data. The true core of the conflict lies in the ancient conception of ritual purity. For this we will repeat some essential points from a general essay on the subject:
In ancient societies, purity codes "are a way of talking about what is proper for a certain place and a certain time...Pollution is a label attached to whatever is out of place with regard to the society's view of an orderly and safe world." It involves "drawing the lines that give definition to the world around us..." More than this: Purity in the ancient world "is fundamentally concerned with the ordering of the world and making sense of one's everyday experiences in light of that order, which is usually conceived as being a divine ordering of the cosmos..."
Ancient cultures like Israel's "draw extensive lines of purity, of clean and unclean, in an attempt to create a model of God's cosmic order and to help an individual locate his or her place in that order so that the person may know when pollution has been contracted and what needs to be done to dispel it, so that access to the holy God and his benefits will remain open." Breaches of boundaries are "unclean". Hence the person partially leprous is ritually unclean; but the person who is totally covered with leprosy is ritually clean. Breaks in the skin or discharges likewise violate boundaries and are ritually unclean. From the Israelites food laws, something like a lobster which lives in the water, yet has legs, is ritually unclean because it breaks the boundaries between land and sea.
Ancient peoples drew what DeSilva [Honor, Patronage, Kinship and Purity] calls "purity maps" in which there was a certain understanding of what belonged where, and what did not. The forbidding of Gentiles into the inner court of the Temple is just such an example, of "unauthorized people trespassing into sacred spaces." Some religious movements follow similar lines of thought today, but for the ancients, this was a way of life inside and outside the religious sphere -- though life and religion were also far more interrelated for the ancients as well.
Thus DeSilva notes that in the pagan world, for example, "(e)ntrance to sacred shrines required that the visitor obey the purification requirements specific to the shrine." These might vary from one cult to the next and could include abstinence, washing of the body, or wearing of certain clothes or a certain style of hair. In reverse, a mixing of the pure with the impure was "expected to bring disaster for the perpetrators and possibly even their race."  Crossing boundaries offended the powers that were.
Of specific concern to us is that in early Judaism, "deeply engraved"  purity maps were drawn distinguishing Israelites from non-Israelites (as well as kosher from non-kosher, and sacred times from non-sacred times). In the time of the NT, Jews were accustomed to thinking of Gentiles as beyond the borders of their purity map; the Zealots went as far as using military action to enforce the boundaries. This was far from politically correct, but it was the norm of thinking for the day.
In turn, purity maps served a group-identity function, clearly distinguishing one group from another in ways that reinforced the group's internal values. The maps were drawn, and kept, with serious intent.
Christianity involved a serious "redrawing" of the purity maps of Judaism. Those who might think that Paul started the fight don't realize that the battle began in the Gospels. Jesus' association with lepers (regarded as perpetually unclean), the dead (Jairus' daughter and the son of the widow of Nain), the demon possessed (ritually unclean), tax collectors, and sinners (morally unclean), and his statement that "Not that which goeth into the mouth defileth a man; but that which cometh out of the mouth, this defileth a man," and his denial of the sacred space of the Temple (John 4 and predictions of the Temple's destruction), involve radical redrawings of the Jewish purity maps, parallel to that which Paul advocated in Galatians 2, but which make Paul's angst shrink in comparison.
And now a key point from deSilva: "The Gospels...present Jesus encountering a stream of ritually impure and potentially polluting people, but in the encounter their contagion does not defile Jesus; rather his holiness purges their pollutions, renders them clean and integrates them again into the mainstream of Jewish society where they can reclaim their birthright, as it were, among the people of God...A critical extension of the principle that God's holiness in Jesus was cleansing and sanctifying the unclean is the early church's discovery that Gentiles could be brought into the people of God without first taking on the marks of the ethnic Jew." [284-5] Let us now understand how this applies to the situation of Galatians 2.
But when Peter was come to Antioch, I withstood him to the face, because he was to be blamed. For before that certain came from James, he did eat with the Gentiles: but when they were come, he withdrew and separated himself, fearing them which were of the circumcision.(2:11-12)
The issue of ritual purity is now clear here. Note that Peter is said to have previously eaten with Gentiles. What has now happened is perhaps that "certain [men] from James" witnessed this "violation" of a purity taboo, this crossing by Peter of a boundary separating the holy from the unholy. (Alternatively, the men from James may not have said anything at all, and Peter may have presumed of his own accord that he should change his behavior -- the fact that Paul does not condemn these men, or James, tells us as much.)
But doesn't this signify two differing ideologies? Not at all, as we shall see; it signifies a problem of social boundaries, which was connected to religion, but that was not the primary issue. It is worth noting that this corresponds with the story in Acts 10 of Peter associating with Cornelius. Peter already had been associating with Gentiles in ways that were taboo according to the purity map of Judaism, and had been criticized for it in the past (Acts 10:24-11:18). Note as well that this has nothing to do with matters of faith vs. works or the identity of Christ, as it stands.
All that is at issue so far is purity mapping; hence as well it is pointed out by Paul that the Jerusalem church did not demand earlier that Titus be circumcised and thereby placed within the bounds of the purity map.
We will discuss more of why the Jerusalem church was so "into" the old purity map in a moment, but for now, it may be noted, as may be expected, that there could easily be extremists who bolstered their position by claiming that salvation was at stake (Acts 15:1, Gal. 2:4). Witherington [Galatians commentary, 152] notes:
One can understand why Torah-observant Jewish Christians would be especially critical of Peter for this sort of behavior. The Jerusalem church had recognized that God had set him apart for missionary work among Jews, and here he was fraternizing with Gentiles over meals which would cause many of those in his target audience to raise questions about his Jewishness. From the point of view of the Jerusalem church, Peter was being a bad witness, and acting in conflict with the character of his calling.
This agrees with a resolution to a related issue: Is Paul In Galatians 2 contradicting his own advice to "become as a Jew" in 1 Corinthians? No -- Paul is speaking in a missionary context of himself; against Peter he is referring to a gathering of the brethren. There was no need for Peter to "become as a Jew" in Antioch, because he was not acting as a missionary and changing his behavior for the sake of clear communication and understanding, but acting as one who was trying to ingratiate himself with others to avoid consequences. What consequences?
Witherington  argues that the consequences were associations with Gentiles that would cause reprisals among Zealots who would consider the less nomistic Jewish Christians to be traitors, just as extremist Muslims today would regard more moderate Muslims as perhaps infidels. The Jerusalem church, in order not to be persecuted into the ground, maintained certain Jewish practices for the sake of not being bad neighbors, as Paul would not be when he became as a Jew for the Jews, or what have you. Hence as well in Gal. 6:12 Paul regards avoiding persecution as the motive of the "false brethren."
It should be pointed out that it is most likely that Paul was not in Antioch at the time the "men from James" came to town (that is, even if they were the direct motivators), and that these men were not around when Paul confronted Peter, and were not themselves the false brothers. Otherwise, it is likely that he would have known the names of these men (though keeping them anonymous may be a shaming device), and also confronted them in the assembly, and said or done something before others were led astray. Much of what is described clearly happened while Paul was in absentia.
In addition, we see also the reason why Paul has spent as much time as he has in Gal. 1-2 defending his apostleship. To confront Peter was a bold maneuver that would have led Peter to lose face if he did not respond to the challenge, unless Paul was indeed Peter's inferior, and could thereby ignore the challenge. As Malina notes in The New Testament World (39), "only equals can play" this game, and only those recognized as equals can play it. If Peter were Paul's superior, he had the power to ignore and even punish Paul for his impudence. (Paul could also do this if he was Peter's superior, but no one argues for that.)
Paul's recounting of his credentials and recognition by the Jerusalem church are not an ego trip, but within the context of an ancient honor-shame society (NOT what we have today) established his right to confront Peter on equal terms, and established the need for Peter to answer the challenge.
Finally, Paul's word for Peter's method ("withdrew") is a military or tactical term describing a retreat to an inconspicuous sheltered position [Witherington, 154]. If this were as much an issue as the critics suggest, surely Peter's "retreat" would have been much bolder and more defiant.
And the other Jews dissembled likewise with him; insomuch that Barnabas also was carried away with their dissimulation.(2:13)
What has happened now is that Peter, the de facto leader of this group, has similarly drawn away others. Under the ancient focus on shame and honor, it became, once Peter stepped back over the line, dishonorable not to follow. Peter and Co. were literally shamed by the group from James (either directly, or by their presence and the assumption of what was expected) into returning to the old purity map, and Peter's actions in turn shamed others into following (including Barnabas, a Levite who would be very sensitive to the apparent need to appear more "law-abiding").
Here again a specific word is important: "dissimulation" means play-acting, or a charade, believing one thing while doing another. The implication again is that Peter, etc. are being inconsistent with their own known position. Indeed, in this light, Paul essentially regards Peter and Barnabas as victims or as careless, not as primarily culpable.
But when I saw that they walked not uprightly according to the truth of the gospel, I said unto Peter before them all, If thou, being a Jew, livest after the manner of Gentiles, and not as do the Jews, why compellest thou the Gentiles to live as do the Jews?(2:14)
Paul's accusation, that Peter and the others did not walk according to the truth of the Gospel, is correct in line with Jesus' own behavior in consistently and defiantly crossing ritual purity lines. Note once again that Paul also notes that Peter "livest after the manner of Gentiles," thus agreeing again with Acts 10-11 that Peter had had previous realization that the purity lines had been redrawn in Christ.
This may also be why Paul does not go after James, even if James and his men were direct motivators: James had never done as Peter did and started living like a Gentile. It is not Torah observation that Paul is against, but inconsistency and hypocrisy. Thus also, perhaps, why the men from James are not attacked, even if they were instigators -- they were not being hypocrites.
We who are Jews by nature, and not sinners of the Gentiles, Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified.
It is this verse above all which leads critics to conclude that here we have a split between faith vs. works, and behind it, Christ as divine vs. Christ as normal guy. But the matter is far simpler. In light of the purity maps, Paul is now making the point that the previous criteria for being within the bounds of the purity map are now gone; the bounds have been redrawn by Christ, and therefore, to behave as Peter did is in effect to deny that "God's order had been breached in the cross of Jesus." Faith and works as Christian ways are not in the least at issue here, much less the identity of Christ.
What is at issue is purity, and the criteria by which others are deemed pure. The implication of the Galatians influencers (see Nanos review linked above) was that purity and membership in God's kingdom was not achieved except by following the old map -- which is why Paul does go on to stress that if that is so, then logically, one must also follow the entire map (5:3), not just part of it.
The implication was that Christ had not purified the Gentiles and redrawn the map, and in turn, implied that Christ's atoning death was ineffectual. Note that there is no indication at all that Peter "worked it through" and would have denied Christ's atoning death (though by Nanos' view, the influencers never were concerned with it in the first place). If that had happened, not sitting with Gentiles would have been the least of things to worry about.
Paul's message to Peter was, "If you do A, then B -- do you realize that?" The influencers were concerned with the surface matter of ingroup signs of membership, and in Jerusalem, probably the pressure of persecution, and a missionary effort, to Jews still under the law -- not with the deeper implications of what they were demanding. At the same time, the idea of the body of Christ having separate members was itself a form of defilement, of separating that which was whole. It really was case of someone "robbing Paul to pay Peter".
Indications are, from Acts and the rest of the NT, that some in Jerusalem did realize the implications of what they demanded, and the result of that is the conference of Acts 15. (It should be noted that the understanding of Gal. 2 is very much interlinked with how it is placed in terms of a chronology with Acts. As we note in the link below, the timing is much better suited if we place Galatians early, and Galatians 2 between Acts 11 and 15. Placing Gal. 2 after Acts 15 is a keystone in any thesis wishing to emphasize the "fight" between Peter and Paul.)
Jesus' denial in John 4 that the Temple at Jerusalem was not the sacred space, but that personal worship was the way to go, is echoed in Paul's reference to the body as sacred space (1 Cor. 3:16-17) which could be polluted, and in Peter and John's recognition that the believer had been made holy in Christ (1 Peter 1:14-16, 1 John 3:2-3) and who should abstain from polluting behavior (as is clear in all the writings of the NT, including Paul's). Paul in later letters apparently has no problem in relating to the Jerusalem church, as he takes up a collection for them (1 Cor. 9:5-6, 2 Cor. 8-9, Rom. 15:22ff, Col. 4:10 -- critics are reduced to suggesting, as Hyam Maccoby does, that this collection was intended as a bribe to the Jerusalem church to accept Paul, or a way of him buying Roman citizenship, which does no more than change the thesis in light of the facts).
Of course this is not to say that some in Jerusalem did not stick by their guns; indeed, we would expect that some would try to strengthen their view by making salvation dependent on nomism, and we may well see the roots of the Ebionite movement in such persons. But it is clear that they were the ultimate losers in the debate, that James was not even by Paul's reckoning guilty of following them, and clear as well that to see such an enormous rift and upon so many issues as the critics suppose is a wish fathering a thought.