That same logic was used with antimiscegenation statutes in the 60's. The states would argue: "Black people can marry, as long as they marry another black person. White people can marry, as long as they marry another white person. But a white person cannot marry a black person."
Of course, we all know, that in 1967 the Supreme Court struck these types of statutes down. Well, some people would then ask... why does the Supreme Court allow statutes that don't allow a man to marry another man; but allow a man to marry a woman?
The current status of our law places 'race' in a 'suspect class' and thus, any statutes regarding race are subject to strict scrutiny. Statutes regarding sexual orientation or same-sex marriage are considered by our courts to be in a different class that requires a less rigorous review than those dealing with race.
In my opinion, the entire marital system worked better before the legislature got heavily involved. But once the legislature got involved, it required involvement from the courts.