" In fact, the church of Antioch was founded by St. Peter and it was there that the terms "Christian" and "Catholic" were first used."
I see in the book of Acts where they were first called Christians at the Church at Antioch but where is it stated that the Antioch Church was founded by Peter or they were called "Catholic" there?
In this letter, he said: Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. (Chap 8). You can see the document here, courtesy of Calvin College.
That Saint Peter, before he went to Rome, founded the see of Antioch is attested by many Saints of the earliest times, including Saint Ignatius of Antioch and Saint Clement, Pope. It was just that the Prince of the Apostles should take under his particular care and surveillance this city, which was then the capital of the East, and where the faith so early took such deep roots as to give birth there to the name of Christians. There his voice could be heard by representatives of the three largest nations of antiquity — the Hebrews, the Greeks and the Latins. Saint Chrysostom says that Saint Peter was there for a long period; Saint Gregory the Great, that he was seven years Bishop of Antioch. He did not reside there at all times, but governed its apostolic activity with the wisdom his mandate assured.