In this segment from Galatians chapter 2, Paul calls Peter out on one very important thing; his prejudices. What does that mean? Peter's life and background was inherently Jewish, and so he was accustomed to Jewish practices, life, and people. When Peter was evangelizing to the Gentiles (in this case, the people of Galatia), Peter hung around with those who were Jewish and were not hanging around those who were Gentiles. This offended the Gentiles, and when Paul went to Galatia, the Gentiles aired their grievances to Paul. So Paul saw this, heard Peter's message, and called Peter out in front of everybody, challenging him on what he's saying. The significance of this is striking. Paul was the most hardcore of Jews, lived a Jewish life, was an authority in Judeo practices, and followed the Law of Moses stringently. Yet when Christ met Paul, He humbled him, and did a work in Him that would change Him forever. From that effort, Paul challenged Peter on what he was saying and doing. What are Christians justified by? Christ crucified and raised from the dead. He did it all. So Paul challenges Peter on why he is compelling Gentiles to live as Jews in his messaging, when that's not the Gospel message, and calling him out to check his prejudices.