How is it a privilege? You could be the worst person in the world and still get married as long as it was a willing adult person of the opposite sex. It's automatically a given, in other words a "right".
It's not set up as a "given" because it's a right. It's set up that way because marriage, as a government institution, is designed to stabilize a growth in population. The purpose of giving marriage a relationship with the state is to pseudo-regulate the production of families. In that right, I wouldn't even call it a "privilege."
Homosexual couples require no regulation because they won't have any surprises.
