Marriage is unlike any other governmental benefit. License to marry carries with it far more than mere permission, as in obtaining a license to drive or practice a profession. The reason that gay-rights supporters are so determined to achieve equal status for same-sex unions, and the reason that so many others vigorously oppose that recognition, is that marriage is an affirmative statement of societal approval.
Congress took account of this fact in enacting DOMA [the Defense of Marriage Act], and of the fact that large majorities of Americans still oppose recognition of same-sex marriages. Significantly, most Americans do not oppose some other form of legal recognition for same-sex couples that isn't called marriage.
"Civil unions. Because you're not a person -- you're a gay!"
Marriage is an example of a social practice that has become so thoroughly conflated with the state that it is difficult -- even for people who love each other bunches -- to imagine undertaking the endeavor without making it "official" in the eyes of virtually everyone.
In the present context, to deny one group of people this "affirmative statement of societal approval" which has become culturally bound to the state can be interpreted in turn as an affirmative statement of societal disapproval as regards those individuals in particular.
Of course, there is always the argument to be made that what is elemental about "marriage" does not spring forth from the blessing of a loveless bureaucracy, but is rather whatever two people and their immediate community can sustain by the force of their own creative design. But this does not mitigate the injustice at the point where it presently resides: within a society that, for now anyway, cannot imagine "marriage" developing toward its most fruitful maturity in the absence of a state.