There is an easy argument for gay marriage that blocks polygamy. Just say Scalia Thomas and Reinquest were right in Lawrence v. Texas and reinstate bower.
As Scalia noted in Lawrence
State laws against bigamy, same-sex marriage, adult incest, prostitution, masturbation, adultery, fornication, bestiality, and obscenity are likewise sustainable only in light of Bowers’ validation of laws based on moral choices. Every single one of these laws is called into question by today’s decision; the Court makes no effort to cabin the scope of its decision to exclude them from its holding.
your argument presupposes we grant a lot of premises but it's not necessarily true that we should.
Let me be clear that I have nothing against homosexuals, or any other group, promoting their agenda through normal democratic means. Social perceptions of sexual and other morality change over time, and every group has the right to persuade its fellow citizens that its view of such matters is the best. That homosexuals have achieved some success in that enterprise is attested to by the fact that Texas is one of the few remaining States that criminalize private, consensual homosexual acts. But persuading one’s fellow citizens is one thing, and imposing one’s views in absence of democratic majority will is something else. I would no more require a State to criminalize homosexual acts–or, for that matter, display any moral disapprobation of them–than I would forbid it to do so. What Texas has chosen to do is well within the range of traditional democratic action, and its hand should not be stayed through the invention of a brand-new “constitutional right” by a Court that is impatient of democratic change. It is indeed true that “later generations can see that laws once thought necessary and proper in fact serve only to oppress,” ante, at 18; and when that happens, later generations can repeal those laws. But it is the premise of our system that those judgments are to be made by the people, and not imposed by a governing caste that knows best.
the bolded parts are the direct refutation of your claim