It teaches them lessons. Horror movies (the goods ones, at least) are morality tales. They're horrifying because they're trying to embody a bad choice or something of the like. When your kids realize that doing something wrong may incite the wrath of a demon, they'll probably be a bit more careful when it comes to the choices they make.
They won't break. Just because your kids watch something scary, it doesn't mean that they'll fall apart. It's fake. They'll know that as long as you explain it to them. Horror movies are actually a great way of showing kids what the difference is between one's imagination and one's reality.
They'll grow up proud of themselves. When they get a bit older and they're around other people who weren't allowed to watch horror movies as kids, they'll definitely feel the pride. They'll feel more matured. More respected. It's a fact.