St. Peter was not head of the Apostles. All the Apostles acted as having the same authority.

The Apostles, as having been sent by Christ to all nations, had universal jurisdiction. But this universality of jurisdiction was extraordinary, and did not pass to those successors whom they consecrated for particular localities. Also, whilst the Apostles each rejoiced in jurisdiction over all regions, St. Peter had all authority centred in him. Hence St. Paul went to consult him at Jerusalem.

Radio Replies Volume 1 by Rev. Dr. Leslie Rumble MSC and Rev. Charles Mortimer Carty