Acts.
Where does the Bible say Peter was the one leader or pope?
Actually, it is more evident in the gospels than in Acts that Peter is the leader not by His own choice but by Godās choice.
In Matthew 16. Jesus promises to build his church upon him after his confession that Jesus is the Christ, the Son of the living God. So Jesus says only God the Father could have revealed that to him. God the Father could have given the revelation to anyone or everyone of the apostles, but no, God the Father Himself singles out Peter. When Jesus made the pronouncement, it was like He was confirming the Fatherās choice.
Notice how in all that confusion (the apostles did not know what to reply to Jesusās question), Peter cuts through all that and makes a proclamation of who Jesus is and what His mission is. The truth about Christ came forth not from Christ Himself but through Peter. And this is the way the Father and the Son through the Holy Spirit WILLLED it.
In Luke 22:31-32 Jesus said: āSimon, Simon, behold Satan has demanded to sift all of you like wheat, but I have prayed that your own faith may not fail; and once you have turned back, you must strengthen your brothers.ā
Why not just pray for all of them? Wouldnāt that have been easier? No, he prays for only one, Peter and he in turn is to strengthen the others.
After the resurrection, both John and Peter go to the tomb but even though John got to the tomb first, he waits at the door till Peter arrives and Peter goes into the tomb first.
John 21 has already been cited. But I want to make this one point. Jesus tells Peter to tend and feed
MY sheep. Not any, sheep but His sheep. So I think one way of finding out whether we are indeed the Lordās sheep is to check who is tending and feeding us. Is it Peter and his successor.
In Acts -
After Pentecost - Peter was the one who spoke out and preached.
At the Council of Jerusalem Peter was the one who spoke out and made the decision regarding circumcision.
When God made the revelation regarding the gentiles (Acts 10) , it was Peter to whom it will be revealed even though it was Paul who would spread the gospel to the gentiles. In Cornelius vision, he was told to summon Peter.
There are many texts in the Bible that prove Peterās primacy
Lastly I would like to pay a closer attention to Luke 5:1-13.
When the crowd was pressing on Jesus at the Lake of Gennesaret He decided to hop onto a boat. There were two but He chose specifically Simonās.
They put out a little bit from the shore and from Peterās boat Jesus started preaching. Think of about that, the word of God is being proclaimed by Christ from Peterās boat. And it will always be the same. The barque of Peter (as the Catholic Church is called ) will always be the one through which the Truth of Christ will be proclaimed.
And notice what happens next, after Christ has preached to the crowd, he tells him to put out into the deep. And after the big catch, after Peterās āLord, depart from me I am sinful manā what does Christ do?
Some of the other apostles were around him at the time as well, but the text goes: Jesus said to Simon, āDo not be afraid; from now on you will be catching men.ā. Notice how the object of that commission is specifically Simon Peter. He could have given the address to everyone, yet He specifically singles out Peter.
I often say that when people have issues with the Catholic Church, it is usually Christ they really have an issue with or more precisely Christās will and choices. In the above references, it is clear that it was Christ who chose Peter to be His prime apostle.