I have a shirt that says the Catholic Church was founded in 33AD. Does this Church claim this? If so, why?
The Catholic Church claims to be founded by Jesus Christ Himself and that He founded His Church on His apostles.
Jesus Christ founded His Church by giving His apostles the power of binding and loosing (Mt 16:19, Mt 18:18). Binding and loosing are terms that denote authority. In Mt 28:19-:20 Jesus told the apostles that they have authority to teach all nations. We see this in Acts 15 when the Apostles are presumed by all to have the authority to settle a doctrinal dispute in the early Church. The Apostles established the hierarchy of the Church: deacons (Acts 6:2-6), priests (1 Tim. 5:17; Jas. 5:14–15), and bishops (1 Tim. 5:19–22; 2 Tim. 4:5; Titus 1:5). And Jesus had set aside Peter and his successors as the earthly head of the Church (Mt 16:18; Jn 21:15-17 ).
Now that we can see that the Catholic Church is the Church founded by Jesus, how do we arrive at the year 33AD? That is the year that most historians believe that Jesus was crucified and resurrected. On Pentecost following Easter, the Holy Spirit came upon the Apostles (Acts 2:1-6) and they began their mission of preaching and teaching the Gospel. Pentecost is considered by theologians to be the “birthday” of the Catholic Church.