I've heard this question, and others that are very similar, more times than I can count. From door-to-door missionaries, from roadside "preachers" telling me to convert to their own "true" religion, to people who are just genuinely curious - my statement that I am a Catholic and am not going to budge doesn't make sense. Even more frequently, I hear people say (and not unkindly), "Oh, you're Catholic... I'll bet that you can't wait to get out of the house so your parents aren't making you go to Church any more."
It's saddening that when I say I'm Catholic, people automatically assume that I'm going to quit my faith as soon as I possibly can. Truth be told, it's the exact opposite.
Most people look at the vast realm of religion and their initial thoughts are either "These people are all insane." or "Every single one of them thinks that THEIR religion is right, and maybe one of them is - but how can I know which one?!"
For me, there are two main reasons why I think my belief Catholic faith is justified.
1) There is more evidence to back the Catholic Church than any other religious denomination that I've yet encountered. (to those reading this who aren't Catholic - please correct me if I'm wrong!)
2) Everything in the Church is logical.
Expanding upon the first reason: the Bible is widely recognized by scientists and historians to be historically accurate. There are a few incidences of questionable nature (such as that the world was created in six days), but the New Testament (the Gospels) is known to be valid. In the New Testment, Jesus states explicitly that he is God, and came to earth to redeem mankind. This is supported by the miracles he performed (facts which, to my knowledge, were not questioned or refuted by people at the time).
Secondly, throughout the ages there have been amazing miracles attributed to Catholic saints. The history books tend to leave these out; but there are multitudes of these miracles, which have been verified by medical professionals (yes, there are still miracles today, verified by our "cutting edge" doctors) to be beyond the realm of human intervention.
Expanding upon the second reason: "faith" and "reason" are in no way separate. There are many religions I consider to be illogical, either in their foundations or teachings. To give an example, I have come across people who say "it doesn't matter what you believe, just so long as you're a good person." That may be - but shouldn't we strive for truth? Take the Muslim and Catholic religions; one says that Jesus is God, the other that he is not. They can't both be right. Does this mean that we shouldn't investigate further or make a decision for ourselves which we think is correct?
That said, I believe in the Catholic Church because its evolution as a religion follows a series of logical steps. The Jews (I won't go into why they're credible, it'd take too long for me to explain every little thing) believed that a Savior - the Messiah, the true King - would come to save them, liberate them, and reopen the gates of heaven for them. Jesus not only fulfilled all of the prophecies, but also said that he was the Messiah - however, the Jews had been expecting a more physical King, one who would also save them from the Romans, not a carpenter's son. The religion that resulted was the original Christianity, Catholicism.
And why I believe that Catholicism is the correct version of Christianity... that requires a separate post.