People against gay marriage are, as far as I'm aware, really just against gay people being considered married by the (Christian) church, because--in their opinion--Christianity has a specific definition of "marriage", and gay marriage doesn't qualify.
It seems to just be a bunch of people talking past one-another. Each group sees their definition of "marriage" ("marriage" as in "legally considered together", or "marriage" as in "accepted as a couple by your local congregation") as the only one that actually matters, and so obviously that's the one their opponents are arguing about as well.