That the Church was built "on Peter" (as Jesus said) is the same as to say it was built on Peter's faith. It was certainly not built on his bones and brain, and neither was it built upon his errors: within the paragraph, Jesus was saying (prompted by Peter's errors) "Get behind me, Satan!"
A distinction WITH a difference. Different words that denote different objects. The Greek shows it plainly and clearly.
The church is built on CHRIST.
If your church isn’t, it’s not the body of Christ. It’s the body of Peter.