Context prior to this verse is Jesus asking who the disciples say He is. Peter replies with the known line of "Christ the living son of God". To which Jesus says he could not have known this of himself but upon this premise he will build his Church.

The premise (Rock) being that Rock of Jesus Christ. Peter founded a church, but so did hundreds of others across history. If it was Peter and only Peter then something went wrong because they merged with the Roman empire upon it's demise.