But marriage is a social institution and thus a PUBLIC matter. The reason a society creates marriage in the first place is because society needs children to survive and the more stable the form of union the more childreen it produces on average (ie women having one night adventures have less children than women living with a man these less on average than married women). That is the reason the society spends resources on creating a legal cadre, keeping records and reducing the taxes paid by married couples.

No society I know about has ever accepted gay marriage and other sterile unions: in Doric regions of ancient Greece men were encouraged to have homosexual relationships as a way to increase army's cohesion but AFAIK even at Thebes or Sparta marriage was a thing who happenned between a man a woman.

Finally, the principle of separation of powers means that judges cannot make the law, only interpret it. And extending marriage is definitely a legislative (ie out of bounds for judges) issue since decisions of a judge don't bind him or bind other judges for other cases.

As I said people can have sex or live with whoever they like, it is their business. But marriage is society's business.