The Pope is the visible head of the Church that Jesus left behind after He ascended into Heaven. Most of us know that Jesus said “You are Peter and on this Rock, I will build my Church” It is in Matthew's Gospel chapter 16 verse 18. Catholics see this as Jesus ordaining Peter as the first Pope, but non-Catholic Christians say that Jesus was talking about Peter’s Faith not his Office.
This passage needs to be understood in the larger context of the chapter. In Matthew chapter 16:17 Jesus tells Peter “Blessed are you Simon son of Jonah” which is clearly a blessing. In verse 19 Jesus gives Peter the Keys to the Heaven and the authority to bind and loose. This is another gift from Jesus. It is therefore logical to recognize that in verse 18 when Simon has his name changed to Peter (Petros which means small rock) in Greek and that he is the Rock (Petra big rock in Greek) that Jesus will build His Church on is also a blessing. Jesus also promises in this verse that the “Gates of Hell will not prevail against it”. If the Church that Jesus founded on Peter has been corrupted, then Jesus did not protect it as He promised. Protestants argue that the Greek words for little rock (Peter) and big rock (Peter’s Faith) mean that Jesus wasn’t talking about Peter personally. The Bible was written in Greek, but Jesus spoke Aramaic and the same word is used for big and little rock in (Kepha in Aramaic) so Jesus was really talking about Peter both times. Some will question Peter’s mistaken grasp at authority in verse 22, where Peter tries to keep Jesus from going to Jerusalem to be crucified. Peter later denies knowing Jesus 3 times as Jesus predicted. After Jesus' resurrection, Jesus restores Peter in his office in John chapter 21 verses 15-17. Here Jesus asks Peter 3 times “Do you Love Me” to restore Peter’s denials. Jesus also tells Peter to feed my lambs, tend my sheep, and feed my sheep. These commands are given to Peter, not the 10 other disciples, and indicate that Peter is to teach new believers, take care of the 10 other Disciples, and to teach the other Disciples.
Peter’s primacy is quite apparent in the New Testament. Peter is mentioned by name more than 100 times. John is second at 29 times. Peter is always listed at the beginning of the list of Apostles or as the leader of the Apostles, even though Andrew was the first Apostle called by Jesus. In the Book of Acts it is Peter who preaches and converts the Jews. He tells them to repent and be baptized to forgive their sins. Peter tells the other Apostles that we have to replace Judas. Peter heals the crippled man. Peter gives out the discipline that kills Ananias and Sapphira for lying to the Holy Spirit and the Church. Peter heals Lydia and Tabitha. Peter receives the vision that it is ok to eat all foods. Peter is the one called to convert Cornelius the first Gentile and his family to Christianity. When there is a dispute about Gentiles needing to become Jews before becoming Christians, Peter gives the final testimony about Cornelius receiving the Holy Spirt without becoming a Jew, so Gentiles don’t need to be circumcised. There is no other discussion after Peter’s testimony and the Jerusalem Council issues a binding decree that Gentiles can be brought into the Church. After Paul’s conversion, he goes to Jerusalem to learn the Faith from Peter and James. Later Paul rebukes someone named Cephas for not eating with the Gentiles in Galatia. Some consider this Cephas as the Apostle Peter, but Eusebius the early Church historian explains this Cephas is another person. Even if it is the Apostle Peter, it only shows that the Pope does not always act correctly, even though he has the authority to teach correctly. The Jews continued to recognize the Chair of Moses where they received authoritative teaching. Jesus told the disciples that they should do what Scribes and Pharisees teach, but do not copy what they do.
When the Jewish disciples heard Jesus tell Peter that He was giving him the Keys to the Kingdom, they recognized the authority of a minister from the dynasty of King David. Jesus is the Messiah that sits on the Throne of David. In Isaiah chapter 22 we learn that a successor of King David named Hezakiah, had a minister named Shebna who is replaced by Eliakim. The authority of the office is shown by the robe he wears and Key he carries. Keys at this time were large so they could reach through thick walls to operate the lock mechanism inside. When Jesus tells Peter that He is giving him the Keys to the Kingdom, Peter and the Disciples knew that Peter would have similar authority. Peter was to become the Prime Minister over the whole Church and the rest of the Disciples would become Ministers in their own areas with authority to bind and loose. The Disciples also recognized the office was handed on to successors as it was in the Kingdom of David. The Book of Revelation chapter 3 verse 7 uses similar symbolism, speaking plainly of Jesus having the key of David in His Kingdom in Heaven. Jesus left Peter behind on earth so that we would have a representative of His to guide the Church that Jesus founded. That office was passed on to successors like the other Apostles passed on their offices to the Bishops.
Around 90AD, the Church at Corinth had a dispute and wrote the Bishop of Rome. Pope St. Clement, Bishop of Rome writes the Corinthians a letter to resolve the problem. The Corinthians may have written to the Church in the destroyed Jerusalem, or the Church in Antioch, or to the Apostle John, but they wrote to Clement of Rome, and it was read in their Church and others at a yearly festival to commemorate the occasion. Around 107AD Ignatius of Antioch writes to the Church in Rome that he does not command them like Peter and Paul did. Ignatius writes that the Church in Rome presides over Christianity. He asks them not to try and save him when he gets there. Around 115AD Polycarp of Smyrna goes to visit the Bishop of Rome about the dating of Easter. Polycarp didn’t go to Jerusalem or any other early Christian city because he knew where the authority was. Around 180AD Irenaeus writes in Against Heresies that all Churches must be in communion with the Church of Rome because of its preeminence since Simon Peter and Paul taught there. In 200AD Tertullian in his Prescription against Heresies writes that there is an authoritative throne of the teaching of the Apostles in Rome. There are many more references later than these.
The Protestant reformers developed their own understanding of the Bible to base their new churches on. There are now thousands and thousands of Protestant denominations with a large variety of understandings of the Bible based on their founder. The Bible Alone does not provide unity.
The Orthodox Churches share much in common with the Catholic Church, but they rely on the decisions of Councils to maintain their unity. The problem they have, is some churches have broken away from the original Catholic Church when they disagreed with the decisions of Councils.
The Catholic Church consists of the Roman Rite and Eastern Rite Churches. They use the Bible that they assembled, the decisions of Councils and the guidance of the Pope to determine doctrine and maintain unity for the last 2000 years. There are 23 different Eastern Rite Catholic Churches that are in union with the Bishop of Rome. They have different liturgies, but hold the same doctrines as the Roman Catholic Church. The liturgy of the Eastern Rite Churches is similar to the Orthodox liturgy and is usually said in Greek. The Catechism describes the Office of the Pope in paragraphs 880 through 887.