You have put your finger on the right issue, but perhaps in a way that fails to answer the concerns of those who oppose gay marriage.
The issue IS "compelling interest" to the government, which as far as I can see when it comes to gay marriage -- the arguments against which are rooted almost entirely in religious faith -- there is none. In fact, the interests we DO have in promoting committed, monogomous, reltionships -- the social welfare which they promote -- are just as accomplished with same-sex partners as they are with heterosexual partners.
That said, those who disagree with what I just wrote, will not be so quickly persuaded. We need to ask what marriage is for, and then see why we might all be agree on how to achieve that. Much more productive that fighting about what marriage is.