I haven’t given the matter too much thought, but it seems to me that calling it a right has to imply some responsibility that is being protected by marriage. In Catholic understanding, that responsibility is primarily “continuing the race”. That’s why the family is hedged around with protections. That’s why we privilege the family, because without it, everything else dies.
The purpose of gay marriage is to demand the same status as a family and, perversely, to punish families that fail to pretend that narcissistic gay couplings are the same thing as a family. The end goal is going to be the attempt to prosecute those who do not believe that such couplings constitute a family and who do not believe the children raised in such arrangements are going to be served well. In short, the claim of marriage as a right for gay will end in the attempted destruction of marriage as a right for anybody.