Sometimes the argument is put forward that Paul’s opposition to Peter in the treatment of gentiles means that Peter didn’t have the authority Catholics ascribe to him. But a closer look at the passage shows this objection doesn’t actually amount to much.
11When Peter came to Antioch, I opposed him to his face, because he was clearly in the wrong. 12Before certain men came from James, he used to eat with the Gentiles. But when they arrived, he began to draw back and separate himself from the Gentiles because he was afraid of those who belonged to the circumcision group. 13The other Jews joined him in his hypocrisy, so that by their hypocrisy even Barnabas was led astray.
14When I saw that they were not acting in line with the truth of the gospel, I said to Peter in front of them all, “You are a Jew, yet you live like a Gentile and not like a Jew. How is it, then, that you force Gentiles to follow Jewish customs?
Here we see that what Paul opposed was Peter’s hypocritical actions, not a failure to teach and hold the correct doctrine. In fact, since hypocrisy consists in teaching one thing and doing another, Paul’s condemnation demonstrates that he and Peter shared the same teaching.
Of course, sometimes this passage is brought forth to demonstrate that Peter was “just a fallible man” like everyone else. But this rests on a confusion of terms. Papal infallibility doesn’t mean that the Pope is free of sin or moral frailty. In fact, the object of infallibility isn’t the Pope himself, but the dogma which the Pope proclaims.
This is very similar to the sort of infallibility that most conservative Christians grant to the authors of scripture. Yes, they were “fallible men,” yet these specific writings of theirs are infallible. Likewise the pope is “just a fallible man,” but these dogmatic proclamations are infallible.