From the grammatical point of view, the phrase "this rock" must relate back to the closest noun. Peters profession of faith ("You are the Christ, the Son of the living God") is two verses earlier, while his name, a proper noun, is in the immediately preceding clause.
As an analogy, consider this artificial sentence: "I have a car and a truck, and it is blue." Which is blue? The truck, because that is the noun closest to the pronoun "it." This is all the more clear if the reference to the car is two sentences earlier, as the reference to Peters profession is two sentences earlier than the term rock.
“From the grammatical point of view, the phrase “this rock” must relate back to the closest noun. Peters profession of faith (”You are the Christ, the Son of the living God”) is two verses earlier, while his name, a proper noun, is in the immediately preceding clause”
First of all, this is English, not Greek. Second of all, Peter identifies Christians as “lively stones,” and each make the same confession as himself that Christ is the Chief Cornerstone. If Christ is building the Church on Peter, and not on Christian faith (by which all become “lively stones” in God’s house) wouldn’t Peter be the Chief cornerstone? Why would Christ be the Chief Cornerstone, the Head of the Church, and yet have a second “Chief” stone on top of Him? The Catholic interpretation also suggests a hierarchy of powers, and yet the Apostles all performed the same miracles, even punishments, and administered the entire Church from one end of the world to the other. Even Paul did not hesitate to correct Peter when he was in error. And guess what? So do all Christians, since we are all a “Holy Priesthood” and “Kings and Priests” to God our Father. Each of us has full access to God to have our prayers answered, our bodies healed, our sins forgiven, and even the Devils have need to fear us. Not for us ourselves, but the Holy Spirit who dwells in each of us, a “Holy Priesthood” and new living temples for God.
One can grant your interpretation of the verse—and initial post too, of Peter being the leading disciple, without having to logically grant any sort of primacy to the Bishop of Rome.
Peter’s link to Rome is tenuous at best, as Linus was the first Bishop of Rome, NOT Peter, and Paul probably spent more time in Rome than Peter anyway—having first addressed his most ambitious epistle to Rome—and later being there for trial under Ceasar under house arrest.
The whole schema of trying to prove the permanent primacy of Rome via Peter came hundreds of years after Peter was martyred anyway. It’s clear it was a post-facto argument, by supporters of the early medieval world’s most powerful city’s Bishop.
Classic Roman Catholic “proofs” here, of out of context verses, and revisionist history. Oh well!
One might want to look at what happens shortly after:
“18 It was at this time that the disciples came to Jesus with the question, Who is really greatest in the kingdom of Heaven?
2-4 Jesus called a little child to his side and set him on his feet in the middle of them all. Believe me, he said, unless you change your whole outlook and become like little children you will never enter the kingdom of Heaven. It is the man who can be as humble as this little child who is greatest in the kingdom of Heaven.”
It seems the disciples also were discussing who had primacy. Jesus could have looked at them sadly and replied, “I told you that just a little while ago”. But Jesus did not. Here is the chance, for all eternity, to reveal who his “Vicar on Earth” is, and Jesus...punts?
Jesus told us who his Vicar would be - the Holy Spirit:
“None of you asks me, Where are you going? That is because you are so distressed at what I have told you. Yet I am telling you the simple truth when I assure you that it is a good thing for you that I should go away. For if I did not go away, the divine helper would not come to you. But if I go, then I will send him to you. When he comes, he will convince the world of the meaning of sin, of true goodness and of judgment. He will expose their sin because they do not believe in me; he will reveal true goodness for I am going away to the Father and you will see me no longer; and he will show them the meaning of judgment, for the spirit which rules this world will have been judged.
12-15 I have much more to tell you but you cannot bear it now. Yet when that one I have spoken to you about comesthe Spirit of truthhe will guide you into everything that is true. For he will not be speaking of his own accord but exactly as he hears, and he will inform you about what is to come. He will bring glory to me for he will draw on my truth and reveal it to you. Whatever the Father possesses is also mine; that is why I tell you that he will draw on my truth and will show it to you.”
- John 16
The first use of the term in reference to the Pope was in the 5th century, and it wasn’t commonly used until the 1200s.