I’ve always gotten a kick out of this passage, for some reason. Disagreement in the church goes WAAAY back. Plus Paul: ain’t afraid to get in somebody’s face.
«But when Cephas [Peter] came to Antioch, I [Paul] opposed him to his face, because he was wrong. He had been eating with the Gentiles before certain people came from James. But when they came, he began to back out and separate himself, because he was afraid of the people who promoted circumcision. And the rest of the Jews also joined him in this hypocrisy so that even Barnabas got carried away with them in their hypocrisy. But when I saw that they weren’t acting consistently with the truth of the gospel, I said to Cephas in front of everyone, “If you, though you’re a Jew, live like a Gentile and not like a Jew, how can you require the Gentiles to live like Jews?”»
(Quick side note, for those who don’t know (like me, a few years ago): Paul was kind of a super-villain, a super-pharisee (if you will) who killed a lot of Christians before he decided to take a road trip to Damascus:
«Meanwhile Saul, still breathing threats and murder against the disciples of the Lord, went to the high priest and asked him for letters to the synagogues at Damascus, so that if he found any who belonged to the Way, men or women, he might bring them bound to Jerusalem.»
Guess who wound up changing his name?)
 “Cephas” was Peter’s name in Aramaic, the language most commonly spoken in ancient Israel at that time. “Peter” is Greek. They both mean “stone” (and they both refer to the same person).
 “Jews” is “Christians who used to be Jews”. Everyone in Israel starts this story out Jewish. Jewishness was the water they swam in; the context.
 I use that word “pharisee” advisedly; it’s tricky, since SOME people who call(ed) themselves “Christians” accuse Jews of being “Christ-killers” (Hitler and the German Nazis, for instance.) However, Saul/Paul studied at the feet of Gamaliel, one of the great Jewish teachers of the time, and he turns out to be quite the theological ninja (Acts 23:6-10, *snerk*), so I think “pharisee” might be fair.