Which biblical passages support the Roman Catholic tradition about St. Peter’s leadership?

The Roman Catholic tradition regarding the leadership of St. Peter, often referred to as the Petrine theory, is primarily supported by three key biblical passages that describe Christ conferring authority upon him.12

Key Biblical Passages

• Matthew 16:18–19: This is considered the most significant passage. Jesus says to Peter, "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".12
• John 21:15–17: Following the Resurrection, Jesus charges Peter to "Feed my lambs" and "Tend my sheep," which is interpreted as a commission to lead the faithful.12
• Luke 22:32: At the Last Supper, Jesus tells Peter, "But I have prayed that your own faith may not fail; and once you have turned back, you must strengthen your brothers." This is cited as evidence of Peter’s role in confirming the faith of the other Apostles.12

These texts are interpreted by the First Vatican Council to signify that Christ established St. Peter as the visible head of the church with true jurisdiction, a role that passes to his successors, the bishops of Rome.1