Here are the passages in 1 Cor 7 that merit examination:
v6: I [Paul] say this as a concession, not a command.
v12: To the rest I [Paul] say this (I, not the Lord)....
v25: Now about virgins, I have no commandment from the Lord, but I give a judgement as one who by the Lord's mercy is trustworthy.
v40: And I think that I too have the Spirit of God.
Let us discuss verse 6. To cite this passage in the context of this objection equivocates the distinction between concession and command with the distinction between inspired and not-inspired. [Note that Jesus Himself in the gospels makes concessionary utterances, for in Matt 19:8 Jesus states that Moses permitted men to divorce their wives because the Jews' hearts were hard. That is, Jesus Himself authoritatively states something concessionary.] Inspiration deals with the origin of the words or ideas of Scripture. A concession or a recommendation can be just as much as a command. Yahweh made a concession to the Hebrews at Sinai concerning divorce, and in the OT prophetic writings Yahweh makes pleas and entreats apostate Israel to come back to Him. These writings are inspired as much as those writings which deal with commands. The objection is confusing the type of texts [command and/or concession] with the origin or Intelligence behind the texts. This is a category fallacy once again. There is no conflict here in v6, accordingly.
Verse 12 looks quite imposing, but it too does not take much effort to investigate. In v10, Paul directly appeals to the teachings of our Lord such as those in Matt 5:32 and 19:3-9. He says in v10: "To the married I give this command, not I, but the Lord." The rest of verses 10 and 11 are restatements and reminders of Jesus' words on divorce.
Now Paul is going to deal with something Jesus is not recorded as dealing with in the gospel accounts: marriage and divorce when one partner is a believer and the other is not. As these words of Paul in verses 12-40 are not issues that Jesus directly addressed [if He did address these issues they are not recorded], Paul states that it is he and not Jesus who is saying these things.
Yet the fact that Jesus was not recorded as physically uttering these words that Paul is giving in verses 12-40 really does not conflict with the orthodox doctrine of inspiration that 2 Tim 3:16 puts forth, for the term theopneustos in that passage, "God breathed", is not restricted only to those words of Jesus. Check the BAGD lexicon or any other lexicon to verify this point.
If inspiration covered only what Jesus Himself said, then we would have a problem. But inspiration does not limit itself to what Jesus Himself said, and the Church has never had this restrictive a view in its history. This objection commits a straw man fallacy by equating the set of God-inspired writings with the set of sayings of Jesus, pointing out that Jesus did not utter the words in verses 12-40, and proclaiming that there is a contradiction.
With verse 12 discussed, the discussion for v25 can be brief. The fact that Paul's judgement in this and following verses is not directly found in the accounts of what Jesus said is no problem with regards to 2 Tim 3:16, for the same reasons in the above paragraph.
Now for verse 40, where Paul concludes with "...And I think that I too have the Spirit of God." Simply put, anybody who claims that v40 conflicts with 2 Tim 3:16 needs to produce a valid argument that having confidence that one is guided by God the Holy Spirit prevents one's words from being God-breathed. Bear in mind also that Paul's letters to the Corinthians are heavy with irony -- which this statement sounds very much like.