The key for defenders of "traditional marriage" is to come up with a rational basis for restricting marriage to one man and one woman. The general argument that opponents of same-sex marriage make is that the state has a rational basis in promoting marriage as an institution devoted to procreative activity. Since only a man and a woman can procreate, the argument goes, this provides a rational basis for restricting marriage to one man and one woman (at a time).
An obvious rejoinder is: what about infertile couples? Could the state prohibit infertile couples from marrying? Obviously not, but perhaps that can be distinguished on privacy grounds. So Justice Kagan put forth a more subtle hypothetical: could the state prohibit marriage between couples over 55 years old?
[Funny this should come up, given this recent post by Mr. Gillete.]
The lawyer arguing against same-sex marriage admitted such a law would be unconstitutional, but tried to distinguish that situation from same-sex marriage. First, he argued that almost all men are fertile until their dying day, so it's very unlikely that both parties to the over-55 marriage would be infertile. Second, he argued that marriage not only encourages procreation, but discourages reckless procreation:
Your Honor, society's interest in responsible procreation isn't just with respect to the procreative capacities of the couple itself. The marital norm, which imposes the obligations of fidelity and monogamy, Your Honor, advances the interests in responsible procreation by making it more likely that neither party, including the fertile party to that ..
[interruption, followed up later with:]
[Marriage is] designed, Your Honor, to make it less likely that either party to that -- to that marriage will engage in irresponsible procreative conduct outside of that marriage.
So the idea is, it seems, that marriage has a purpose even when the woman is no longer fertile because the marriage norms of fidelity and monogamy discourage "irresponsible procreative conduct outside of that marriage" by the still-fertile male spouse.
But why isn't this an argument for same-sex marriage? Gays and lesbians are of course just as fertile as heterosexuals, and they do have children. If the institution of marriage is essentially about norms of monogamy and fidelity, which are enforced to prevent irresponsible procreative conduct, why wouldn't allowing gays and lesbians to marry be just as likely to prevent irresponsible procreative conduct?
Indeed, many gays and lesbians get married to members of the opposite sex and have children with them, only to have those marriages break apart when it is discovered that the marriage is based on a fundamental lie. Allowing same-sex marriage would seem to make this less likely, and thus promote this supposedly essential function of marriage.