"impossible" to demonstrate: that recognizing gay marriage causes some tangible harm.
Dale, I take it that the scare quotes mean that you're not sure its impossible to establish tangible harm.
Let me count the ways...
1) Demotion of Husbands, Wives, Fathers, and Mothers to Partner A, Partner B, Parent A, and Parent B. (Are we male oppressors guaranteed the A label -- at least in hetero partnerships?) A demotion in rank is a tangible harm and gives rise to a legal claim. It also completely transforms human society by abolishing those status names but that may not be tangible harm.
2) Children in government owned and influenced school systems will be taught that whether you marry or not is irrelevant and that the sex of who you marry is irrelevant and that your sex is irrelevant (and that you must not use 'sex' in sentences like that you use use 'gender'.) Some of this has been happening anyway but it will accelerate.
3) This state-generated "gender dysphoria" will cause tangible damage to children and adults.
4) SSM will increase the number of intentionally fatherless or motherless children. A tangible harm except for those who believe that neither fathers nor mothers are significant factors in the development of children. See the confusion induced by 16 years as the child of lesbians: Growing Up With Mom and Mom "It took me a lot of struggle to realize that I really was attracted to men, yet now it is really hard for me to deal with men as human beings, let alone sexually." There was more along those lines -- Ry was intrigued but "repulsed" by heterosexual relations, afraid of the "sexist soul-losing domain of oppression." Her parting thought: "I cannot understand or relate to men because I am so immersed in gay culture and unfamiliar with what it is to have a healthy straight relationship."
5) SSM increases gay acceptance. Gay acceptance increases gays. 75% of gays are left wingers (based on the '04 vote for John Forbes Kerry). Left wingers cause tangible harm to me and to society. Aside from the obvious tax and regulatory damage; left wingers are more likely to commit murder, suicide, and other crimes and are more likely to take government jobs and go on the dole than right wingers.
6) SSM represents a claim that same-sex relationships are equivalent to opposite-sex relationships. That gay marriage=straight marriage. Since the term marriage refers to the melding of diverse characteristics (as in the marriage of different wine grapes), SSM can't be the same as OSM. Government recognition of SSM codifies the lie of the equivalence of these very different relationships. The spread of loose definitions corrupts both language and law. Corruption of language and law causes tangible harm. It should be possible to maintain the distinction between genuine and meretricious relationships.
7) State licensure represents a tangible harm because it costs money and is a form of state regulation. Extending licensure to a previously unlicensed activity extends the harm. Had the residents of the states during the first half of the 19th century realized that the state takeover of domestic relations law would result in the marriages of men and women, they would have left dom rel with the churches where it belongs.
8) SSM will destroy the public schools as the 60% of the population that belong to religious faiths opposed to SSM withdraw their children. Oops! That's not tangible harm. BTW, try to avoid parallels between interracial and intrasex marriages. Exogamy was practiced by most human societies from time to time. Intrasex marriage was not even invented until the Reagan Administration. It's possible that not enough people will pull out to destroy the government schools but the opposition should be aware of the fact that intrasex marriage is a bit more significant for religious believers than earlier secular interventions like prayer bans and sex ed.
9) SSM, though it did not create, will increase government mandated firings for politically incorrect speech which favor only one side of the kulturkampf. Thus 20 years ago since queer marriage didn't exist I couldn't have used the term in a sentence and now I can be fired for it. Reducing employment opportunities for traditionalists is a tangible harm. It would be one thing if the government stayed out of these disputes and let us work them out for ourselves but since CRA '64 governments have been interfering in private relationships (employer-employee, buyer-seller, etc.). Just another expansion of the coercive state apparatus -- a tangible harm.
10) SSM harms libertarianism because it has caused many libertarians to advocate state licensure of a private act. They will, thus, be less able to argue against other forms of state licensure in the future. (Don't get me started on libertarian advocacy of government subsidy of scientific research or of the concept of state sovereignty.)
11) Mod sexual relationships of all kinds (including SSM) reduce child bearing. We need more children and an increasing population. Societies with fewer children are older, will have few workers, lower GDP, less international influence, and may (e.g. Europe and Japan) risk disappearing. The future belongs to those who grow up. We should be encouraging growing populations of bourgeois children who can continue our society. A thin gruel of a few progressive, sexually disphoric children will be insufficient to preserve and extend our society.
12) Massive societal changes may argue-ably be necessary when significant parts of the population, say blacks at 13% are involved. The small sliver (those who want to marry) of the small sliver (1.6%) of the population who are homosexual is not large enough to justify massive social transformation.
13) SSM is always and has always been legal. No polity (even those that punished sodomy with death) criminalized SSM. In the past, that was because SSM hadn't been invented. Persons of same sex affection married all the time when they wanted to produce heirs or unite families. But they married members of the opposite sex to do so. Marriage is an act performed by the couple themselves. Even sacramental marriage in the most orthodox Christian churches is a sacrament in which the sacramental act is performed by the parties. It is, in fact, the only sacrament that is performed routinely by lay persons (baptism can be performed by the laity but it is best done by clergy.) So persons of same sex affection are, and always have been, free to marry.
14) When I read that "there are 1,138 statutory provisions in which marital status is a factor in determining benefits, rights, and privileges" my stomach turns.
I've got a million of them but that's enough for now...