Do gays have the right to marry? Yes. They do not have the right to call something other than marriage, marriage. Reality cannot be conformed to individual whims. I do not have the right to marry my dad. I do not have the right to be legally considered something other than a human being. Politics cannot mandate that triangles are actually squares while maintaining the definition of both.

Same thing here: if same sex marriage could ever be like marriage in such a way that privileging it would not undermine actual marriage, you might possibly be able to make the argument that they can and should be held equal. But humans being what they are, that will never be, even if it is not strictly true that it “must” be so.

Traditional marriage should be privileged over other arrangements because it is the only type of family formation that both can produce children and provide partners for the most people.

It’s obvious that you need at least one man and one woman to produce children. The second part relies on the fact that the vast majority of polygamous societies practice polygyny, or one-husband-many-wives. Since the birth rates of boys and girls are roughly equal in the natural state, polygyny produces a society with surplus men, who will not have a reason to channel their masculine aggressiveness into providing for a family. It will tend to result in chaos, either internally, costing the state in stability or crime, or will be harnessed by the state and used against its neighbors in the form of a military.

Since the state or civilization should want to continue, it should obviously encourage reproduction. Since the state or civilization should want to be stable and get along with its neighbors, it should promote internal stability. Traditional marriage is the only form of family formation that satisfies both of these requirements, therefore it should be privileged by the state over other forms of family formation.