Why is the Catholic Church apostolic? The Catholic Church is apostolic because it was founded by Christ on the apostles and, according to His divine will, has always been governed by their lawful successors.
And I say to thee, thou art Peter, and upon this rock I will build my Church, and the gates of hell shall not prevail against it. (Matthew 16:18)
How do we know that no other church but the Catholic Church is the true Church of Christ? We know that no other church but the Catholic Church is the true Church of Christ because no other church has these four marks.
Further reading: CCC 857-865