The proof lies in the fact that the Catholic Church alone corresponds exactly to the exact religion established by Christ. Now the Christian religion is that religion which— (a) Was founded by Christ personally; (b) Has existed continuously since the time of Christ; (c) Is Catholic or universal, in accordance with Christ’s command to go to all the world and teach all nations; (d) Demands that all her members admit the same doctrine; (e) Exercises divine authority over her subjects, since Christ said that if a man would not hear the Church he would be as the heathen. Now the Catholic Church alone can claim— (a) To have been founded by Christ personally. All other Churches disappear as you go back through history. Christ said, “Thou art Peter, and upon this rock I will build my Church.” There are many claimants to the honor of being Christ’s Church. But among all non-Catholic Churches, we find one built on a John Wesley; another on a Martin Luther; another on a Mrs. Eddy, etc. But the Catholic Church alone can possibly claim to have been built on Peter, the chief of the Apostles, and one-time Bishop of Rome. (b) To have existed in all the centuries since Christ. (c) That every one of her members admits exactly the same essential doctrines. (d) To be Catholic or universal. (e) To speak with a voice of true authority in the name of God.
The true Church, Question 327 from Radio Replies Volume I Copyright © 1938 (by Rev. Dr. Leslie Rumble, M.S.C. and Rev. Charles Mortimer Carty).