Paul confronted Peter about his comradely with other Jews and the distance he was showing towards the Gentiles. The Gentiles were offended by this because they felt alienated by Peter. You see, Gentiles were messy, messed up people to the point where even their worship involved prostitution in their practices. That said, it was very difficult for Peter to deal with people of this nature, act out his ministry with grace (by showing it) and, in a way, "undo" the influence of the Jewish way of life and the Jewish, Godly approach to things that he had all his life. But what does this all boil down to? Jesus can work wonders when you are justified by Christ alone. And the catalyst to that is faith: putting your faith in Christ and letting Christ live through you, as Peter had to learn. .