Oh, there's a mechanism all right. But gay marriage opponents usually can't be pressured into stating it -- either because they don't want to admit thinking the way they do or because they're convinced they would draw even more anger and ridicule than they already have.
Actually, there are two. One -- which they will sometimes explain in public -- is that allowing gay people to marry their partners is one more step toward society's acceptance of gay sexuality as a normal human variation. For someone who's convinced that gay sexuality is irretrievably sinful AND inevitably linked to debauchery, drugs and pederasty (none of which is true, of course) it's important to prevent ANY step toward normalcy, less the supposed adjunct practices also become normal and approved parts of society (since, to them, treating something as normal applies actual approval -- very black and white thinking).
The one most opponents won't admit to is that, to them, the conventional nuclear family is THE building block of civilization (totally ignoring the role of business relationships, voluntary societies, churches, friendship, and any other human relationship). The reason? Because growing up in a nuclear family is THE place where you learn, and internalize, submission to authority. Children obey their parents. Wives (in some people's view) obey their husbands. But gay marriages would be, in their view, inevitably marriages of equals, with no one in authority over another. THAT'S what they are most afraid of -- that without early training in authority and submission, society will cease to function because people will stop obeying.
(The possibilities of cooperation, collegiality, consensus, compromise, and negotiated agreement seem to go right over their heads.)
The nuclear family is a very recent innovation... and it occurs to me that someone who writes as coherently as you is perfectly aware of that, so I'm'a shut up about it.
It seems to me that what they want is communities where everyone's pretty much like everyone else. Villages, really. It is terribly useful, politically, to have villages.
I am unable to remember if I was the one who first said this; it's been too long:
It takes a village to raise an idiot.
I think there's also a sense that, if people the anti-marriage folks disapprove of are allowed to join in the marriage game, it will somehow lessen the value of marriage as an institution. If those icky people can do it, marriage must become ickier by association. The "logic" breaks down the more you start questioning it, but I think that's the basis of at least part of the anti-marriage stance.
I didn't say I didn't know the excuses the anti-gay-marriage folks use--but that they were invalid logic and lacking a causal connection. The "value of marriage as an institution" can be seen either as "the value that married people--as opposed to single people--contribute to society" or "the value that society allows to married people in return for the supposed value added by married people."
Societies have valued marriage for multiple reasons: it's seen as stabilizing adults (they "settle down" in pairs instead of roaming around seeking partners for casual sex) and as providing stability (economic as well as other) for children born to that union. It can link families in cooperative groups, define inheritance of property, etc. Societies that see marriage as providing stability and order consider this "the value of marriage as an institution"--its value to society. In that sense, refusing to allow gay persons to marry forces them into what society considers a less desirable lifestyle, and promotes the very behaviors that society considers undesirable in heterosexuals. Refusing to allow them to marry costs society the benefits society gets from stable adult sexual pairs (even if only serially stable.)
In this country (and many others) married persons have some privileges the unmarried do not have, such as a right to inherit (some) property, a right to know about a spouse's medical treatment and make decisions about it if that spouse is incapacitated, and certain tax benefits. These privileges and benefits are intended to encourage marriage...and these are a tangible part of "the value of marriage as an institution" to the married persons. It has occurred to me that what the opponents of gay marriage are really on about is the monetary benefit of marriage, which they prefer to keep to themselves. But that's painting them slimier than they may actually be. There's still no believable (to anyone but themselves) mechanism that transfers the presumed "ickiness" of the gay couple getting married to the straight married couple. That's like saying that no straight person can eat a food or drive a car or wear any garment style that a gay person ever ate, drove, or wore...which is ridiculous. I'm sure there are gay people who eat chili, barbecue, bread, cheese, tomatoes, apples, etc., who drive every brand of car on the market including a Ford Clubwagon or Dodge Caravan, who wear jeans, trail shoes, T-shirts...and a lot of straight people who eat, drive, and wear the same things without any ickiness transfer.
I think there's a third reason, which if stated, would blow up in their faces even worse:
The consider marriage a *privilege*, not a right. And they don't want the privilege extended to people they disapprove of.
Pretty much the same applied to inter-racial marriages and before that to inter-faith marriages.