There actually is a reason that authoritarian types feel that same-sex marriage detracts from straight marriage, but it's not the kind of conscious thing they can tell you about.  They just "know" that doing it differently from "the regular way" hurts "the regular way". 

What it is is that authoritarian types often have what sociologists call an external conscience.  This means that they rely on the community around them to enforce their morals, as they haven't internalized them enough to do it themselves. (This is the basis for the idea that it's not really wrong until you get caught....) The only way this external conscience business really works is if the whole community shares the same rules.  So what they are really objecting to is others having different rules.  It makes the whole system crumble because it's no longer clear what morals are being enforced.  This lack of clarity is experienced as very threatening because they need and want the community to keep them on the straight and narrow, since they can't do it themselves.  So, this change in the rules really is threatening. 

Not that I'm sympathetic to this way of thinking, but I've studied it some because it's interesting and I wanted to know. 

So, in summary, from their very different world view, having new and different rules really can be very threatening, while the threat is completely invisible to the world view of someone with an internal conscience.