New International Version (NIV)
18 And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it.
I guess it all boils down to how you translate Greek. We as Protestants choose to believe as does this commentator that we as believers are His Church.
The name Peter (Gk., Petros) means “rock” or “rock-man.” In the next phrase Christ used petra (upon this rock), a feminine form for “rock,” not a name. Christ used a play on words. He does not say “upon you, Peter” or “upon your successors,” but “upon this rock”—upon this divine revelation and profession of faith in Christ.