No one says he was.
As leader of the Christian community in Jerusalem, he was host to the council convened there by the Apostles. No one would deny this. That he has the "last word" recorded in Acts 15 on the issue is not much of a surprise for the same reason; as host, he would have a last-word summation of the meeting. This sort of thing happens all the time in conferences today.
This is your personal opinion of what happened at the Jerusalem council, but it's not what St. John Chrysostom says about it:
This (James) was bishop, as they say, and therefore he speaks last...There was no arrogance in the Church. After Peter Paul speaks, and none silences him: James waits patiently; not starts up (for the next word). No word speaks John here, no word the other Apostles, but held their peace, for James was invested with the chief rule, and think it no hardship. So clean was their soul from love of glory. Peter indeed spoke more strongly, but James here more mildly: for thus it behooves one in high authority, to leave what is unpleasant for others to say, while he himself appears in the milder part.
Chrysostom, Homilies on the Acts of the Apostles, Homily 33
Peter was not the leader of the entire church, either. All the Apostles were regarded as equal in authority. Chrysostom says, "The Apostles were designated rulers, rulers who received not nations and particular cities, but all being entrusted with the world in common."
(Inscriptionem Actorum II. PG 51, 93)
Cordially,
Diamond,
We've been around this quote from St. Chrysostom just the other week. I pointed you to the homily on Matthew 16, where Chrysostom does call Peter chief of the apostles. Do you remmeber the discussion? Should I find the relevant quotes?