Why do Catholics say they are His Church?

I have seen in a number of posts Catholics referring to themselves as His Church, the true church. Every church should be His Church, not just the Catholic church. Jesus did not establish the Catholic church which many people say not only is this is not scriptural, it is not historically evident. With the Catholic church so into tradition shouldn't they get the tradition right? The first Christians were a Sect of Judaism, not Catholicism. Catholicism was birthed out of paganism and apostasy.