Let’s talk for the record, Catholic Teaching (courtesy of The Question Box by Rev. Bertrand Conway):
Tertullian:
“Peter, who is called the rock wherein the Church was to be built, and who obtained the keys of the kingdom of heaven.”
St. Cyprian:
“Peter, whom the Lord choose first, and upon whom He built His Church….” and again “[Peter is] the rock and foundation after Christ.”
The summation being that Christ was the Divine Founder of the Church, its Rock primarily; Peter was the rock secondarily, by divine appointment.
(This is in line with my previous statements that Christ is the Cornerstone and Peter is the foundation.)
So; are you trying to show disagreement between church fathers?
What rationalization, all supported by the opinion pieces of Catholic *early church fathers.*