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But when Cephas came to Antioch, I opposed him to his face, because he stood condemned. For before certain men came from James, he was eating with the Gentiles; but when they came he drew back and separated himself, fearing the circumcision party. And the rest of the Jews acted hypocritically along with him, so that even Barnabas was led astray by their hypocrisy. But when I saw that their conduct was not in step with the truth of the gospel, I said to Cephas before them all, “If you, though a Jew, live like a Gentile and not like a Jew, how can you force the Gentiles to live like Jews?”. - Galatians 2:11-14
Paul explains here the way the hypocrisy is playing out. Peter is eating with the Gentiles as though he does not recognize anything wrong with that activity; in fact, he already knows directly from God that all foods are now clean. When some men (Jews) come from James, Peter draws back and separates from eating with the Gentiles as though he now does recognize something wrong with that activity.
Peter's hypocrisy then was in fearfully altering his behavior depending upon what crowd he was in rather than steadfastly holding to the truth he had directly from God. His behavior was not in keeping with the truth he proclaimed.
While Peter was still saying these things, the Holy Spirit fell on all who heard the word. And the believers from among the circumcised who had come with Peter were amazed, because the gift of the Holy Spirit was poured out even on the Gentiles. For they were hearing them speaking in tongues and extolling God. Then Peter declared, “Can anyone withhold water for baptizing these people, who have received the Holy Spirit just as we have?” And he commanded them to be baptized in the name of Jesus Christ. Then they asked him to remain for some days. - Acts 10:44-48
This caused other Jewish believers and even Barnabas to be led astray and it was serious enough to cause Paul to oppose Peter personally like a good brother should.