Like my post on Tuesday, this is just a general overview. There are a multitude of other reasons, but these are the three I would put forth to someone who asked me this question but didn't have several hours to discuss. And like the other post, these are not arguments that are universal for all Catholics. They have other reasons.
1. I believe it is the church Christ intended to leave. This includes two thoughts - one is that Jesus intended for their to be an organized church, and also the Catholic church is in fact this same church. On the first point, I think we can find several places in the New Testament that point to an organized church that isn't just local. There are people in charge and a plan. When they have questions, they go to a higher authority on the chain of command, such as when they went to Jerusalem to get the opinion of the apostles on circumcision.
I think Jesus makes it pretty clear Himself in Matthew. And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven. And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven. (Mat 16:17-19)
Peter means rock, and a literal reading would indicate Jesus is naming Peter rock and stating His church will be built on Peter. It doesn't say Peter's faith, it doesn't say the faith of all the apostles. Just Peter. Keys are an idea also in Isaiah 22, in reference to a prime minister post. He's delegating authority here to His prime minister. There's a lot more going on here, but I want to be brief.
There are only a few churches claiming to be this same church Jesus established. I'm only familiar with the Catholic Church and the Orthodox Church. If one believes Christ intended an organized church like the one I'm describing, then that really only leaves two options.
2. I believe in the Eucharist. In John 6, Jesus talks about His flesh being literal bread. He doesn't stop those who take this time to leave Him by noting it is spiritually intended; not literal. He uses words that indicate literally chewing. Throw in the letters that indicate how important Communion is, and I don't believe it is a symbol at all. We have very early writings from Christians discussing the literal presence of Christ in the Eucharist - this isn't some sort of developed idea.
This isn't surprising or problematic for me in the least. The God who created the universe can surely turn bread and wine into body and blood. How? I don't need to know.
Again, if one believes this, there are only a few churches to choose from. Catholic, Orthodox, Anglican (I think), and Lutherans (at least some).
3. Open the Bible to the Table of Contents, where it lists all the books of the Bible. That text is not divinely inspired. Nobody has ever claimed that God specially designated them personally to be the writer of the Table of Contents; to pick which books would end up in the Bible.
Let's skip the Old Testament here as we don't agree on which books go there, but every Christian has the same books in the New Testament. Some of them are obvious choices, but some were contentious choices. Some books that existed and were popular at the time were left out. On whose authority were the books selected? How do we know that the Bible we have in our hands is full of books that are actually divinely inspired?
There would have to be some guarantee on the people that picked the books. That can only come from one place. Either the Church had the authority to determine the books in the New Testament, or the book you currently hold in your hands could have the wrong books in it. I'm not talking about the particular translation or anything - I mean the individual books could be wrong. James could be entirely uninspired. Paul could have been a heretic who simply wrote enough letters they were bound to be included.