That makes zero sense. You're trying to see what you wanna see.<quoted text>
They miss the point of Matt. 16:18 all together:
13 When Jesus came to the region of Caesarea Philippi, he asked his disciples,“Who do people say the Son of Man is?”
14 They replied,“Some say John the Baptist; others say Elijah; and still others, Jeremiah or one of the prophets.”
15 “But what about you?” he asked.“Who do you say I am?”
16 Simon Peter answered,“You are the Messiah, the Son of the living God.”
17 Jesus replied,“Blessed are you, Simon son of Jonah, for this was not revealed to you by flesh and blood, but by my Father in heaven. 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.
The subject is Peter's confession that Jesus IS the Messiah, the son of the living God. The confession is the Rock being discussed.
The truth is that the Catholic Church didn't launch because they read Matthew 16:18 nor any certain Biblical verse. They existed for almost 40 yrs before the Gospel of Matthew was even written.