JESUS was the Rock, not Peter. He was a pebble, a shepherd for the flock. There IS no indication in Scripture that Peter was Pope.
However, it is VERY clear that Jesus set up Peter as the head of his Church, and it is also logical to assume that Peter would set up a successor.
Apostolic Succession is a concept accepted by the vast majority of Christians. The only difference, on that point, with Orthodox and Anglican would be the Papal authority.
Make no mistake, even the Orthodox recognize the Pope as the Bishop of Rome, and authoritative as a Bishop.
What do you think Jesus meant by telling Peter that he could bind and loose things on Earth and in Heaven?
What ELSE could those words possibly mean?
Tradition is as important a tool, for the Faith, as Scripture.
The Early Christians had to meld Jewish tradition with Early Christian tradition. We can only guess, sometimes, at how this was done. There is scripture, to be sure, to help in some areas. However, when the various parts of the New Testament were written, not a single document really acknowledges all of the other documents, or Books.
It is more than likely that many of the Sacred works of the Apostles, many of their notes and writings, have been lost forever.
Scripture is helpful, but not all inclusive of what comprises faith. Historical facts, such as the fact that Jesus did not object to prayers for the Dead, the fact that Jesus prayed for Lazarus, the fact that Jesus never objected to Maccabees as part of Sacred Scripture, in the Temples where Jesus prayed to His Father -— these things speak louder than words.
Then, we have the ACTUAL words of Jesus, words like “Build” -—
What country elects a leader without a successor?
What company can survive without a successor?
God gave us brains.
God expects us to read between the lines.
(Of course, in your case, you have to read the lines themselves, first!)
“Peter you are rock and upon this rock I will build my Church” “Whatsoever you bind on Earth shall be bound in Heaven, whatsoever you loose on Earth will be loosed in Heaven.”
Jesus would not use these words for any other reason than to make Peter head of the Church.
It is logical to assume that Peter would set up a process for his successor, which he did.
Jesus gave Peter this power, by his very words.
And please don’t get into the Greek translation stuff. Jesus spoke in Aramaic, and there is no gender difference, for “rock” in that language.