It is better not to argue with people about religion. An intelligent discussion that is seeking understanding can be enlightening, but most religious arguments are no more intelligent than a repeated "I'm right, you're wrong", like two dogs barking at each other. There is no point in using the Bible texts like stones that we throw at each other. That is a mockery of what God's word should be for us, and is not, frankly, very Christian. But if people from the sects accuse you of corrupting Christian teaching, remember that as Catholics we have plenty of support in the Bible for looking to the Holy Father for guidance in our faith. It is our critics, not us, who have a hard time justifying themselves. Be confident!
The Church is likened by Christ to a "mustard seed" that grows and develops, so we cannot expect to see in the pages of the Bible all Christian teachings fully developed and as visible as they are now. However, we can certainly see that the Catholic teaching on the primacy of Peter is drawn from New Testament.
The importance of Peter is shown by the fact that he is mentioned by name 195 times in the course of the New Testament. The next most-often-mentioned is John, just 29 times. When the names of the Apostles are listed, Peter is always first. Judas Iscariot is always last (Mt 10:2-5; Mk 3:16-19; Lk 6:14-17; Acts 1:13). Sometimes Scripture simply speaks of "Simon Peter and the rest of the Apostles", or "Peter and his companions" (Lk (:32; Mk 16:7; Acts 2:37), showing that he had a special role that represented all the apostles as a group. Often Scripture shows Simon Peter as a spokesman for them all, as if he were the voice of the Church (Mt 18:21; Mk 8:29; Lk 8:45; Lk 12:41; John 6:68-69).
"Now when Jesus came into the district of Caesarea Philippi, he asked his disciples, 'Who do men say that the Son of Man is?' And they said, 'Some say John the Baptist, others say Elijah, and other Jeremiah or one of the prophets.' He said to them, 'But who do you say that I am?' Simon Peter replied, 'You are the Christ, the Son of the living God.' And Jesus answered him, 'Blessed are you, Simon Bar Jonah, for flesh and blood has not revealed this to you, but y Father who is in heaven. And I tell you, you are Peter; and on this rock I will build my Church, and the powers of death shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.' Then he strictly charged the disciples to tell no one that he was the Christ." (Mt 16:13-20)
In Acts 10 Simon Peter receives a special revelation from God that Gentiles are to be welcomed into the Church without having to follow the Jewish laws and be circumcised. In Acts 11, he welcomes the first Gentile converts in the name of the Church. In Acts 15 it is Peter who delivers the revelation concerning non-Jewish believers. St. James, the bishop of Jerusalem, appears in a position of leadership alongside Peter. While James delivers the pastoral, disciplinary teaching, it was Peter who delivered the binding doctrinal teaching. His primacy was recognized by St. Paul when he describes in Galatians 1:18 how he went to see Peter to make sure his teaching was in line with Peter's. From the earliest times onwards, recourse has been had to the Bishop of Rome to settle disputes and - in the words of one early writer - to "preside the charity of the Church".