Mat 16:16 And Simon Peter answered and said, Thou art the Christ, the Son of the living God.
Mat 16:17 And Jesus answered and said unto him, Blessed art thou, Simon Bar-jona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.
Mat 16:18 And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.
The "this" in "this rock" alludes to Peter's name.
It is correct that Jesus is saying Peter is the rock upon which he will build his church. Jesus is saying , in the words of Albert Barnes (protestant theologian) “Thou art a rock. Thou hast shown thyself firm, and suitable for the work of laying the foundation of the church. Upon thee will I build it. Thou shalt be highly honored; thou shalt be first in making known the gospel to both Jews and Gentiles.”
That Peter is or is not the rock is not the argument with Catholicsm. The point where Catholicism gets it wrong, is attributing it to the person of Peter alone, too much, and also not considering that it was the 12 apostles who were foundational not just Peter (Rev 21:14), and that all 12 apostles were granted the authority and keys, not just Peter (John 20:23, Mat 18:18). Although Peter was a chief apostle, Christ did not purpose, to exalt Peter above the others, as Catholics suppose, and there's many passages of scripture which show the equality of every apostle. In fact it is God's very humble nature not to intend to have one person exalted over the other as "the world" does, as we see today in the papal system in the Roman Catholic heirarchy.