At the conclusion of the Jerusalem Council (Acts 15), not only did Peter, James and John confirm that Paul preached the true Gospel, but they also acknowledged him as the apostle to the Gentiles, just as Peter was the apostle to the Jews. Thus, they perceived that Paul was an apostle of the first rank, of equal status to themselves. On that basis they publicly offered him the right hand of fellowship, signifying they were partners together in the Gospel. Their only request was that he remember the poor, a reminder that the Gospel of Grace should naturally bring forth good works. However, later when Peter visited Antioch, Paul had to confront Peter publicly, because his behaviour was undermining the Gospel of Grace. By not eating with the Gentile believers, Peter was implying that there was something lacking in their justification and full acceptance by God.
Oxford Bible Church - Living in the Last Days (audio)