Dahlia Lithwick explains the rationale to uphold the ban on same-sex marriage in Washington State succinctly:
Only if the ban was enacted by insane people can it fail constitutional review.
Burt prejudiced people? No problem. Lithwick adds this rhetorical zinger:
Even the most deferential review should grapple with whether banning gay marriage really encourages straight marriage; whether there is something about marriage that magically lures heterosexual parents into its grasp — something that would evaporate if it were also extended to gay parents. Even deferential review that was also deaf, dumb, and blind would do more than just assert that gay marriage is illegal because kids "thrive" in straight homes. That claim is not just slightly over- or underinclusive, as the majority would have it. It's nonresponsive. Or, as the dissenters put it, better than I have: "denying same-sex couples the right to marry has no prospect of furthering any of those interests."
There is no rational relationship between banning gay citizens from civil marriage and promoting heterosexual marriage and the interests of children. There is no reason why you can't do both. At least I have yet to read a logical argument as to why you can't.