Why did the early church leaders call their church the catholic church?

Answer 1

It was called the Catholic church because it was, and is, a universal church. The word "catholic" is from the Latin catholicus (universal). The term "Catholic Christians" dates from the establishment of Christianity as the official church of the Roman Empire in 380 AD.

It is called the "Roman Catholic" church because the Holy Father, as the representative of Jesus on earth, starting with Peter the Apostle, has always been in Rome. For some centuries the Pope lived in France, but the center of the church was still considered Rome.

Roman Catholic AnswerThe word is derived from Greek and simply means universal. In combination with the word "church" it essentially merely indicates one of the marks of the church, and was so used by St. Ignatius of the beginning of the 2nd century; but in the course of history it has come to be the distinguishing epithet of the Church of Christ and his faith: under other circumstances its place might have been taken by "apostolic" or "one". The use of the word in this distinguishing way became current and common in England only from the middle of the 16th century. In some mediaeval translation of the Creed unam sanctam catholicam et apostolicam ecclesiamis rendered "one holy apostolic church general."

from A Catholic Dictionary, edited by Donald Attwater, second edition, revised.