Banning gay marriage does not "discriminate against a group of people by denying them rights enjoyed by other groups." Under such laws, a gay man can marry a woman but not another man. A non-gay man has exactly the same rights. Whatever may be wrong with traditional marriage restrictions, it isn't equality [Ken Blanchard, "Same Sex Marriage & the Constitution," South Dakota Politics, 2008.11.11].
An anonymous interlocutor (vocabulary is another reason I like Dr. Blanchard) contends that marriage bans constitute unequal treatment under the law by denying homosexuals the right to marry folks with whom they are "physically compatible." I agree with Dr. Blanchard: That's not the best standard to which to appeal. Blanchard suggests that if "physically compatible with" means "physically attracted to," the state already imposes similar restrictions on incestuous or polygamous relationships.
The anonymous interlocutor appears to be thinking about sex, and if I know anything, it's that people tend not to think straight when they think about sex.
To disagree with the good professor, I will appeal not to lust, but to love, to the intentional choice that a free person can make to commit to a relationship with one significant other. That is a valuable, character-building, society-leavening choice. That commitment is about much more than what we do with our naughty bits. It's about sharing a household, raising children, tending each other when sick or dying. Incest and polygamy may still fall under the purview of responsible government, as those behaviors entail problems with power and submission. But if two rational citizens want to make a lasting commitment to each other, we should not contort our law or Constitution into denying that choice.