Matt. 5:17-18 Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil. For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.
Skeptics point to this one and say: "How can this be the case? Jesus broke a bunch of laws from the OT -- or told people to break them."
Did he? Here are the examples I have seen cited, and the answers.
Matt. 15:1-3 Then some Pharisees and teachers of the law came to Jesus from Jerusalem and asked, "Why do your disciples break the tradition of the elders? They don't wash their hands before they eat!" Jesus replied, "And why do you break the command of God for the sake of your tradition?
One Skeptic accuses Jesus of ignoring his own guilt in lawbreaking with a "you do it too" excuse. But Jesus is not breaking the OT law; he is violating a "tradition of the elders" - part of the Pharasaic oral law, or code of interpretation, not the actual law. Jesus' own reply is a typical rabbinic response which points out that his accusers are guilty of a greater offense, which is a violation of the clear law (to honor one's parents) for the sake of a lesser interpretation of the law (Corban).
Attempts to interpret the law after this fashion resulted in peculiarities: For example, one could borrow something as long as they did not ask to borrow it (for that would constitute a transaction, and hence work); one could put out a lamp to save one's life, but not merely to turn it off to save oil; a man could not put vinegar on his tooth for a toothache, but he could put vinegar on his food -- and if he happened to get relief from that, it was OK. [Raymond Brown's commentary on John]
Luke 6:1-4 One Sabbath Jesus was going through the grainfields, and his disciples began to pick some heads of grain, rub them in their hands and eat the kernels...
Jesus is accused of both violating the Sabbath and stealing corn. Once again, however, he is violating a Pharasaic interpretation of what constituted "work", not an actual OT law, and his picking of corn from the fields of the others is allowed in the OT (Lev. 19:9-10) and is not considered to be stealing.
Matt. 15.11//Mark 7:15. These words alter or ignore no Jewish law; they merely stress the obvious point that it is the disobedience, not the food itself, that is the essence of the violation. (The interpretive comment in Mark 7:19 can be seen as a significant alteration in meaning.
However, there are strong reasons to doubt that it is part of the original text: The participal construction hangs awkwardly with no obvious syntactical connection to what surrounds it; the word "foods" is a hapax legomemon (not found anywhere else in the NT); and Mark's usual method of making such "side comments" is entirely different. [Guelich's commentary on Mark, 378])
Luke 11:37-8. This does not record a violation of any law, since while such washings as indicated are described, they are not prescribed or ordered. Indeed, the whole issue for the Pharisee would be the expectation that Jesus would wash after being around the "unclean" masses in the previous passage. In essence Jesus is defying the Pharisee's personal bigotry against the common people.
John 5:8-11. The comment by Jesus' opponents may be reflective of later Mishnah rules that forbade carrying things, especially beds, on the Sabbath, but these are merely interpretations of the "no work on the Sabbath" rule, not actual law.
Mark 2:18-20. This does not involve any sort of Jewish but merely reflects a voluntary ceremonial practice (it is not associated with any of the normal fast days of the Jewish calendar). Matt. 5:32 is no alteration of the law but an interpretation of the law, one the reflects an interpretation also held in first-century Judaism of the day.
Prov. 30:5-6, Rev. 22:18-19. Because the Proverbs verse is a proverb, and therefore no absolute, and because the Revelation verse refers only to the book of Revelation, these cannot technically be used against Jesus or anyone as an indication that one could not add to or "alter" the OT law.
Moreover, not only does this ignore the fact that ancient law codes were not "fixed" and absolute in the same sense as our modern laws, but were rather didactic in nature, it also ignores the fact that Jesus, as God's representative, was perfectly free to update the law and was also the one best qualified to interpret it. However, as we have shown, no actual instance of this has been proven.
John 8:4-11. See our answer here.