Five verses after the verse you cite (Matthew 16:18), Christ refers to Peter as Satan, not on the side of God but of men (Matthew 16:23). Christ would not build His church on a foundation on the shifting sand of human frailty.
Jesus Christ was the Rock on which the Church was built as the Chief Cornerstone of Ephesians 2:10, not Peter.
But don’t take my word for it — take Peter’s, in 1 Peter 2:7 (”the stone which the builders disallowed, the same is made the head of the corner”).
We all sin, right?
Huh? The “stone” Jesus mentions was HIMSELF!
“Whatsoever you bind on Earth will be bound in Heaven”
“Whatsoever you lose on Earth will be loosed in Heaven”
In the same passage where Jesus says “Peter You are ROCK and Upon THIS ROCK I will build my Church”
Peter was the head of the Early Christian Church, PERIOD. And tradition tells us that Peter was involved in the selection of his successor to the Throne of Peter.