Once you make an argument based on the 14th Amendment as the majority did, it opens the door to multiple other arguments like polygamy.
Via Politico:
Welcome to the exciting new world of the slippery slope. With the Supreme Court’s landmark ruling this Friday legalizing same sex marriage in all 50 states, social liberalism has achieved one of its central goals. A right seemingly unthinkable two decades ago has now been broadly applied to a whole new class of citizens. Following on the rejection of interracial marriage bans in the 20th Century, the Supreme Court decision clearly shows that marriage should be a broadly applicable right—one that forces the government to recognize, as Friday’s decision said, a private couple’s “love, fidelity, devotion, sacrifice and family.”
The question presents itself: Where does the next advance come? The answer is going to make nearly everyone uncomfortable: Now that we’ve defined that love and devotion and family isn’t driven by gender alone, why should it be limited to just two individuals? The most natural advance next for marriage lies in legalized polygamy—yet many of the same people who pressed for marriage equality for gay couples oppose it.
This is not an abstract issue. In Chief Justice John Roberts’ dissenting opinion, he remarks, “It is striking how much of the majority’s reasoning would apply with equal force to the claim of a fundamental right to plural marriage.” As is often the case with critics of polygamy, he neglects to mention why this is a fate to be feared. Polygamy today stands as a taboo just as strong as same-sex marriage was several decades ago—it’s effectively only discussed as outdated jokes about Utah and Mormons, who banned the practice over 120 years ago.
Chief Justice Roberts recognized this as a potential problem in his dissent:
I do not mean to equate marriage between same-sex couples with plural marriages in all respects. There may well be relevant differences that compel different legal analysis. But if there are, petitioners have not pointed to any. When asked about a plural marital union at oral argument, petitioners asserted that a State “doesn’t have such an institution.” But that is exactly the point: the States at issue here do not have an institution of same-sex marriage, either.