I don't believe Lord Jesus ever intended for an institution of church to be established and I believe His true church existed before men ever sought to institutionalize it and that His true church still exists today, independent of both catholic and protestant institutionalization. I also believe there are many true followers of Lord Jesus who are also within these institutions, but that most who are "submitted" within this church system are dividing a portion of the Lord's Lordship between Him and the institution of church.
I do not interpret the scriptures as Jesus appointing Peter as the first pope of the catholic church. Peter is not the rock upon which Jesus built His church, but the revelation of Peter acknowledging Jesus as the Son of God - and Jesus Himself - is this rock.
Matt 16:13 Now when Jesus came into the district of Caesarea Philippi, He was asking His disciples, “Who do people say that the Son of Man is?” 14 And they said, “Some say John the Baptist; and others, Elijah; but still others, Jeremiah, or one of the prophets.” 15 He *said to them, “But who do you say that I am?” 16 Simon Peter answered, “You are the Christ,the Son of the living God.” 17 And Jesus said to him, “Blessed are you,Simon Barjona, because flesh and blood did not reveal this to you, but My Father who is in heaven. 18 I also say to you that you are Peter [which means rock], and upon this rock [play on words here, "your name means rock and upon the 'rock' that is the revelation you just had that i am the Christ, the Son of the Living God and the rock that is me (Jesus Himself)] I will build My church"
Other scripture clearly substantiates this including the idea of the believer building our house on the solid rock foundation that is JESUS and no other scripture even hints at Peter being this foundation, an idea which is completely antithetical to the gospel message.
To interpret this scripture as Jesus saying that Peter is the rock upon which Jesus will build His church and that Peter is the first pope, is a colossally false misunderstanding upon which the Catholic church is built. To make peter or the catholic church our foundation is a colossal error when it is Jesus Himself that must be our foundation.
continuing... and the gates of Hades will not overpower it. 19 I will give you the keys of the kingdom of heaven [no longer is Jesus speaking only to Peter, but this is for all of His true followers as clearly indicated throughout other parts of the gospels] and whatever you bind on earth shall have been bound in heaven, and whatever you loose on earth shall have been loosed in heaven. [true for every true follower/disciple of Lord Jesus with prayers in alignment with God's will] ”
20 Then He warned the disciples that they should tell no one that He was the Christ. [this revelation that is the rock upon which His church is built]. If Peter had just been made the foundation upon which the Lord's church was built, Lord Jesus would have been warning the disciples to tell no one that Peter is the new pope.