“This is wrong.”
Nope. Even many Protestant scholars don’t agree with you.
D. A. Carson:
... on the basis of the distinction between “petros” and “petra,” many have attempted to avoid identifying Peter as the rock on which Jesus builds his church. Peter is a mere “stone,” it is alleged, but Jesus himself is the “rock,” as Peter himself attests (1 Peter 2:5-8). Others adopt some other distinction: e.g. “upon this rock of revealed truth- this truth you have just confessed- I will build my church.” Yet if it were not for Protestant reactions against extremes of Roman Catholic interpretation, it is doubtful whether many would have taken “rock” to mean anything but Peter.
... Had Matthew wanted to say no more than Peter was a stone in contrast with Jesus the Rock, the more common word would have been “lithos” (”stone” of almost any size). Then there would have been no pun- and that is just the point!
Oscar Cullman:
... the parallelism of “thou art rock” and “upon this rock I will build” shows that the second rock can only be referring to the first. It is thus evident that Jesus is referring to Peter ... to be the foundation of his “ecclesia.” To this extent Roman Catholic exegesis is right and all Protestant attempts to evade this interpretation are to be rejected.
If such is true, then it is evident that the Church is without foundation as Peter is dead.
To assert otherwise is to assert that this rock
can [and does] change, that is what the apostolic succession means in functional terms.