The universal Church (ekklesia) of Jesus Christ is only one church (ekklesia), regardless of what denomination of organized hierarchy they adhere to.
The Catholic hierarchy like the Pharisees have seated themselves on a seat they have no business occupying. So your argument is inane.
Ephesians 4:14-16
14 As a result, we are no longer to be children, tossed here and there by waves, and carried about by every wind of doctrine, by the trickery of men, by craftiness in deceitful scheming; 15 but speaking the truth in love, we are to grow up in all aspects into Him, who is the head, even Christ, 16 from whom the whole body, being fitted and held together by that which every joint supplies, according to the proper working of each individual part, causes the growth of the body for the building up of itself in love.
NAS
I don’t see Peter or any human being referred to as the head of the universal Church of Jesus Christ in any Scripture.