But, I think it is addressed through Fourteenth Amendment and Equal Protection.
This is where people get tripped up.
If you want to apply Equal Protection then you have to do it on equivalent terms.
You can't simply say gay people have the right to get married. Of course they do. Believe it or not, that is not the issue. The question of relevance to whether it is an Equal Protection issue or not is: WHO can they can they marry? They answer for them is the same as for everyone else: they can marry a member of the opposite sex.
Now you could question the fact that they can't marry someone they love, but that is a vagueness that really can't be legislated. Marriage isn't now, nor has it ever been dependent on love and neither has divorce been dependent on it. People get married for many reasons other than love, and I have personally seen couples that were in love get divorced despite it. I also recognize that your ability to have a relationship isn't guaranteed just because you love them or even if you love each other.
So the simple question comes down to: is a different legal criteria applied to gay people getting married than for straight people getting married. Since the same restrictions and priviledges apply to both (they can both only marry the opposite sex) the answer has to be "no, they are both treated the same under the law".
That being said, I am all for gay marriage and have advocated openly for it with family and friends. I just don't think this argument is a good one from a legal standpoint and would argue against trying to fit this square peg into the round hole of the decision you want. It is more likely to break at least as much as it fixes in the long run.