From the Gospel for the Mass of Twenty-first Sunday in Ordinary Time (Courtesy: USCCB):

And so I say to you, you are Peter,
and upon this rock I will build my church,
and the gates of the netherworld shall not prevail against it. 
I will give you the keys to the kingdom of heaven. 
Whatever you bind on earth shall be bound in heaven;
and whatever you loose on earth shall be loosed in heaven.”

Peter’s original name was Simon. Jesus changed it to Peter, derived from the word for rock. 

Protestants who dispute the Catholic Church’s claim the Peter was the first Pope, or that Peter, himself, was the authority on which Jesus builtthe Church, often claim that it was Peter’s confession of faith that Jesus built the Church, not Peter, himself.

This completely ignores that fact the Jesus literally renamed Simon: “Peter,” his new identity is that of “the Rock,” followed by the literal declaration that it is upon this rock I will build my church. Not, the “Rock’s faith,” but, literally, “the Rock,” itself, Peter. 

And we know that Leo XIV, the current person taking the role of Peter’s authority, is, in fact, Peter’s successor. Now? Recall in the Acts of the Apostles Peter gathered them all togethe to decide who will take the place of Judas. It seemed that the authority and position that Judas had, needed to be transferred onto someone else, because Judas was dead. His body was no more, and his soul had likely gone to Hell. (Strongly implied, although no explicit declaration has been made.) So, if the Traitor Judas needed to be succeeded by the Apostles electing Matthias, then most certainly did Peter. 

If authority rested on mere conviction or declarations of faith, then anyone can assume the authority; which we see is presumed upon in non-Catholic Christianity; heretics are claiming aithority they don’t have and establish new denominations all the time. They don’t have anyone exerting any means to stop them. 

But if authority rests in a person, it’s a whole other matter. It’s one thing to say that authority rests on some immaterial conviction which anyone can claim; but in a person,  it’s different. If it rests in a person, then someone has to bestow or confer the authority on him. Where does the authority come from? The answer tell you. An immaterial conviction of faith can lead to “I can establish a Church based on my interpretation of Scripture.” But if the authory to lead a Church rests not in such a thing, but in the physical person (combined with their faith) then the authority has to be conferred. Authority of this kind is not naturally a part of the human nature, or else everyone can be Pope.  (Authority of any kind is not naturally a part of the human nature, but some can be assumed by the person, others have to be conferred.)

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