Why did Paul oppose Peter in Galatians?

Galatians 2:11-13 - Now when Peter had come to Antioch, I withstood him to his face, because he was to be blamed; for before certain men came from James, he would eat with the Gentiles; but when they came, he withdrew and separated himself, fearing those who were of the circumcision. And the rest of the Jews also played the hypocrite with him, so that even Barnabas was carried away with their hypocrisy. [NKJV]