The analogy of the Loving v. Virginia, was to show that no American citizen will denied their right to marry a person of their choice regardless of race. Once again, the key words are the –“right to marry a person of individual choice”.
No. Once again, the key words are "regardless of race." Loving was (primarily) a race issue, not (primarily) a marriage issue. It wasn't against the law for either one of them to be married. Just to be married to each other. BECAUSE OF THEIR RESPECTIVE RACES.
Nowhere in the 14th Amendment is there a reference to sexual orientation. No protections are guaranteed to anybody based on who they prefer to have sex with. The (legal) claim of gay people is that they are covered under that Amendment. That they have certain "civil rights" protections under that clause. And that simply isn't true. "Gender" is not the same as sexual orientation. And gay people are protected from being discriminated against by "gender" (just like every other citizen). But they want special consideration for the fact that they want to have sex with someone of the same gender (unlike the majority of citizens in the United States .. or anywhere else in the world, for that matter).
I suspect the reasons you don't see the difference between a person's race, their gender and their sexual orientation is because you just don't want to. The differences in definition really aren't all that hard to grasp. Legally, I question whether or not sexual preference is a substantial enough criteria upon which to base legal justifications and modifications - especially to the Constitution of the United States. Personally, I'm not sure it's all that serious an issue. And CERTAINLY ... CERTAINLY not nearly as substantial as the issue of race.
There is no comparison, IMO, between the two. And I don't think I can make myself any clearer about that than I already have.