This is kind of tied in with the Judaeo-Christian worldview, which says that sex is only designed to be done within the context of an unbreakable covenant (marriage), because it bonds you together in a deep way. Sex isn't just an act, which is why divorce is so traumatic. Children are supposed to be conceived out of an act of love into a safe, loving environment. (Everyone is aware that this is often not the reality, but this is what the design is.)

All that is hard to explain, though, so it's easier for people say "it's morally wrong because God says so," which really isn't a helpful or even appropriate way of interacting with non-Christians. An appeal to authority doesn't work if the other person doesn't accept the authority...

Obviously, you are free to reject this view. You can even reject the moral part, but I think that fundamentally the conservative stance is taking responsibility for the consequences of your actions. We take a dim view of people who get drunk, drive, and kill someone, because driving carries a responsibility. So why are we okay with people who have sex and then kill someone to get out of their responsibility?

Hopefully this makes the pro-life position more understandable, even if you don't agree.