There are at least a dozen reasons why Peter was not designated to be the foundation of any church, including that he was not determined to be Catholic until about 445 A.D. Even early Catholic Church leaders such as Eusebius, Chrysostom and Hilary of Arles taught the same disclaimer. The statement about Peter was made to support claims of the primacy of the church.
Matthew 16:18 states, "And I say to you, that you are Peter, and upon this rock I will build my church, and the gates of Hell shall not prevail against it." This is cited as proof. But there are at least three interpretations of "upon this rock" that Peter is "this rock," that Peter's faith in Jesus is "this rock" and that Christ is "this rock."
Peter's name is petros, a small stone, movable, comes apart into pieces. Christ is petra, a large, fixed, immovable rock. Jesus Christ is the foundation of the church (Ephesians 2:20). Even Peter identifies Christ as the foundation.
This is why sola Scriptura is important. "For the time is coming when people will not willingly listen to sound teaching, but having itching ears they will accumulate for themselves teachers to suit their own passions" (2 Timothy 4:3). The principle is well-suited for these times, as well-meaning people just assume validity of oft-stated beliefs.
GORDON A. CASE II