Where is the pope in the Bible?

Matthew 16:18-19. "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." Jesus renames Simon Kepha ("rock" in Aramaic; Petros in Greek), and builds the Church on him. Renaming in Scripture marks a new mission (Abram to Abraham).

The keys are an office. Isaiah 22:20-22 describes the king's steward who holds "the key of the House of David," with authority to open and shut. When the steward died, the key passed to a successor. Jesus deliberately echoes this: Peter is the steward of the Kingdom, and the office outlives the man.

Peter's primacy throughout the New Testament. He is named first in every list of apostles (Mt 10:2 even says "first"). He speaks for the Twelve. Jesus prays for him alone that his faith not fail and tells him to strengthen his brothers (Lk 22:31-32). The risen Christ commissions him three times: "Feed my sheep" (Jn 21:15-17). He leads the choice of Judas's replacement (Acts 1), preaches at Pentecost (Acts 2), and settles the first great controversy (Acts 15:7).

The early Church recognized it. Pope Clement of Rome intervened in Corinth's affairs around 96 AD while the apostle John was still alive. St. Irenaeus (c. 180) said every church must agree with Rome "because of its preeminent authority" and listed the popes from Peter. St. Cyprian called Rome "the chair of Peter."

What the papacy is not. The pope is not impeccable (sinless) and cannot invent doctrine. Infallibility protects him only when defining faith and morals for the whole Church (CCC 891), a power used rarely. His job is to guard the deposit of faith, not to add to it. He is the servant of the servants of God.