Ephesians 2, 20 says that the Church was "...built on the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone..."

Peter did indeed have a special place amongst the Apostles - he was, for lack of a better word, the spokesman. He was not the head of the Church. Again, if your case holds water, then why did James preside in Acts, and why did Peter get overruled regarding circumcision?