Gregory's ServerI think this is right, AND that there is a second motivation.
The prominent right-wing homophobes are gay men who do not believe in straight men. To them all men are gay, but only the weak admit to their desires.
Projection means they believe everyone’s experience is like theirs, ie men wanting men. Therefore if society were to allow men to marry each other, it really would mean the destruction of humanity because literally no one would choose to have hetero sex.