"Before 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." NIV translation
Now, Paul describes the problem that he had with Peter and is was simply that he was acting one way around the brothers in Antioch but another way when others showed up. In this church at Antioch, the Gentiles would eat all kinds of food that the Jews were forbidden to eat by the Mosaic Law. Peter, a Jew, knew that he was no longer under the law and that he could eat anything (because of his vision in Acts 10) and so he joined the Gentiles at the table and ate as they did. But, when the Jews from the church in Jerusalem showed up, he would not eat with the Gentiles. We, as Christians, need to be consistent in our walk and in our freedom. When someone tries to put us back under the law, we need to stand up and proclaim our freedom in Jesus Christ.