Part of the boogyman behind the 'threat' of same sex marriage is a cocktail mix of:
- general social disorder
- setting 'bad examples' for the children
- allowing children to be raised by gays thus 'ruining' their childhood
- a vague but worrying 'devaluation' of hetero couples unions, in a social sense if not legal sense.
- a direct challenge to biblical 'law' and placing the primacy of the bible as singular roadmap for the life of man (for the people who are heavy into the evangelical thing)
- latent anxiety born out of a conservative culture which demonizes sex and sexuality: being gay strongly implies that sex is for social bonding (and fun!) outside of procreation.
etc, etc.
Basically, while there's no rational threat to straight married people from gay marriage, the subjective, social factors are numerous. Mostly it all boils down to the status quo of society being upended in a way that hits home - the basic notion of what a family unit is. It's easier to demonize LGBT people and project all one's insecurities onto them, than it is to stop and ask ones self just why the notion of same sex marriage is unsettling.
Remember, for people who have grown up absorbing the latent social memetics of conservative sectors of society, there's still a lot of queasy unease about homosexuality, period. It has been treated as a sexual perversion and a "dirty" thing for too long and the taint and stigma of that association still lingers even if at a subconscious level for a lot of people. Gay is a 'seedy' concept for some people, even if they lack the language to explain why. The Freudian slips that sometimes happen are telling... being gay is associated directly with lack of sexual maturity or control, with sexual predation, uncleanliness, and bad moral character.
It's relatively easy to incite moral panic by setting the baggage homosexuality has upon an institution like marriage, which (perhaps hypocritically given its failure and divorce rate) is still held up as a beacon for society and literal symbol of purity and purpose.
In this sense, there is a truly massive generational change incoming. People under 30 today have massive advantage over the previous several generations in terms of their exposure to people who are LGBT, and have experienced this at a young enough age that reality has an easier time winning out over inherited cultural memes.
One must wonder how many people in the current over-40 generations are going to end up as That Embarrassing Grandparent in a couple of decades. You know, the future equivalent of the grandpa who makes everyone really uncomfortable at the table, when he starts going on about how he won't "buy a Jap car, because the Japs are putting bombs under the trunks to blow us up, cuz their still tryin' ta get us, just like all their spies we locked up durin' the war, the ones what was pretendin' they wuz Americans."
(This last is a real person. A friend's grandfather, who never misses a chance to warn people that their Japanese branded car has a bomb, and the "Japs" are waiting for their chance to take over.)