Galatians 2:11

But when Peter came to Antioch, I resisted him to the face, because he stood condemned.

He stood condemned ... Far from being infallible in matters of doctrine, the apostle Peter, who is alleged to have been the first pope, here committed the most fundamental doctrinal error imaginable, upsetting completely the false teaching of Peter's supremacy. Peter was not merely condemned by a fellow-apostle, he was self-condemned, his own conscience reproving and repudiating his actions. Paul stated in Romans (Romans 2:1) the principle that holds a man self-condemned if he practices what he condemns in others. This Peter did, for he advocated eating with Gentiles in Acts 10; but here he refused to do so.

Before going any further with this said failure of the beloved Peter, it should be brought to mind that this was only a momentary thing. As Halley put it:

It took a few years for the apostles to get adjusted to the new teaching; and Paul adjusted more quickly than Peter did. The Galatian incident happened after Paul had come all the way out of Judaism, and while Peter was coming out. But Peter did come all the way out before any of the books of the New Testament were written, and there is not an iota of difference between the teaching of Paul and Peter in the New Testament.[26]

Paul was compelled to relate this for reasons which were no doubt providential. The utter condemnation of all the arrogant claims of the historical church regarding the supremacy of Peter, his infallibility, and their own alleged succession to such prerogatives is accomplished by this narrative, as well as the practical thing at hand, in which Paul used it to defend his own apostleship.