Let’s recall Ginsburg’s argument in favor of gay marriage:
Same-sex unions would not have opted into the pattern of marriage, which was a relationship, a dominant and a subordinate relationship. …
There was a change in the institution of marriage to make it egalitarian when it wasn’t egalitarian. And same-sex unions wouldn’t — wouldn’t fit into what marriage was once.
There are two problems with this reasoning. First, equality of the husband and wife regarding their rights to dispose of property and even regarding custody of children does not entail any other kind of equality. For example, perhaps sexually, the wife ought to be “surrendered.”
Second, there are in general not 2 human relations, hegemonic dominance / subordination and equality, but 3, with the addition of complementarity.
We see this most easily in the market, where people specialize within the system of the division of labor. People’s skills complement each other; they can be more or less sophisticated; they earn their owners different amounts of money. Thus, people are unequal both as producers and as consumers; but neither do they rule or submit to each other.
St. Thomas likens this special relationship to “works done by art; for the roof of a house differs from the foundation, not because it is made of other material; but in order that the house may be made perfect of different parts, the artificer seeks different material; indeed, he would make such material if he could.” (ST, I, 47, 2, reply 3)
Similarly, straight marriage features the relation of both bodily and spiritual yin-yang complementarity which gay marriage does not; a reason why they are relevantly different in order for society to recognize one and spurn the other.