Surprisingly to some, these purposes held little or no weight in the US legal conclusions. The fact of state-sanctioned marriage was accepted by everyone and not under debate. Rather it was a matter of equal protection under the law. And one of the law's great purposes is to negate the influence of any one set of personal values and opinions in favor of equality under the law for everyone. The fact that no one could come up with a sound legal reason for excluding one class of people from state-sanctioned marriage is instructive.
Well, it's undeniable that regardless of whether one is homosexual or heterosexual, one was always entitled to lawful matrimony. Matrimony can't be homosexual, nor can the sacrament of holy matrimony (which I obviously don't believe in) be homosexual, for the obvious reason that both require the ability to confer to one party the capacity of being a mother, hence the Latin root. The legal benefits of lawful matrimony were open to any legal person regardless of whether they wish to engage in the ritual or sacrament of matrimony, or marriage in the form of civil partnership, or at least that was the case in most of the commonwealth and many states - in some of which it is still the case. The question fundamentally comes down to not redefining matrimony, for one cannot, the term has a priori heterosexual assumptions, but rather, changing all marriages to non-matrimonial marriages, therefore rendering all marriages civil partnerships. Really, the onus would be on the party wishing to engage in this rather bureaucratic and strange transformation to prove why this is meaningful or fair in any sense, and not upon the party wishing to maintain a traditional institution. It is not simply a question of equality under the law, since that was already maintained for every legal person, it is a question of why partakers in matrimony should be subject to having their ritual treated equally to civil partnership - because clearly they are neither equal nor the same.
This is narrowing the meaning of "arguments against it" to mean only legal arguments that influence legal conclusions, rather than the broader debate over the issue. The purposes perceived to be behind the institution of marriage often drives debates over whether the legal conclusions that were reached were desirable or not. These purposes also still do influence the legal debates because marriage provides unequal treatment of certain couples under various laws compared to the treatment that others receive in terms of things like property rights and taxes. Several classes of people are still excluded from the ability to opt for this special treatment, such as blood relatives or groupings of more than two people. Excluding these groups from the special property and tax treatment enjoyed by others seems to assume some kind of purpose behind the law to justify why such an exclusion would be made.
This is precisely the case. The simple fact that not all people are equal, and certainly that not all people have an equal relation to all other people, either in the eyes of the law or naturally, should make it obvious why arguments that only rely upon equality simply can't hold water. People must be treated with discrimination and delicate appreciation for their situation and status, to do otherwise would be injustice.