Because they go against the law of God as well as natural law. We see often throughout the Bible that homosexual acts are "abominations to the Lord." Homosexual sex and sexual actions are a horrible mockery of Holy Matrimony as well as the union between Christ and His Church.
Simply because you may struggle with same-sex attraction does not mean that you can or should act on your impulses. We are all called to practice chastity according to our state in life.
Homosexuality is not a choice, first of all, this question is essentially like asking "should we jail everyone for being Hispanic?", which I would not be surprised to see on this stupid website. I have a feeling straight conservatives would throw an absolute hissy-fit if they saw a question like this, but asking if we should jail straight people instead.
I am against homosexuality but it is a mental disorder, not criminal. However, what should be criminalized is making other people gay or making them accept it. No one is telling gays to stop being gay but most gays do tell straight people to be gay or to accept it. Let them decide if they want to support it or not, don't shove it down their throats.
You would require a justifiable argument outside of religion to make any case that homosexuality is wrong, and simply you won't find any because what two consenting adults do with their body parts is their own business. Anyone who thinks it should be criminalized is a major bigot who deserves to be sent to a theocratic regime where it is criminalized.
To criminalize how someone feels is wrong. While I disagree with what ThinkFirst said about criminalization of homosexuality being for religious institutions, I do agree that no one simply sits down and says, "You know what? I'm going to be gay. That'll be fun." Nobody does that. Instead, people sit down and say, "Oh. Looks like I like other guys/girls, even though I'm also that gender. Oh well. I guess that's who I am." Making homosexuality a crime is basically like making being straight a crime. It's just how people feel. Don't be prejudiced, people. That's not the right thing to do.
A person's sexual attraction is not something that is chosen. It is something that is discovered. Just like being attracted to blondes, skinny, chubby, blue-eyed, long-legged, etc. No one sits down and DECIDES to be homosexual. It's something they DISCOVER. Criminalization of this is for religious institutions, not rational humans.