Your arguments are weak, and very weak at that.
It's not a right. Who says so? You?
Actually the right to marital privacy has been a part of the US Constitution since Griswold v. Connecticut, 381 U.S. 479 (1965)
I mean, that's a long time. 50 years next year, and somehow people are still having this right peed upon by others.
Those who are denied marriage. Children. Yeah, because right and responsibilities are limited in minors. I don't see gay people having their rights and responsibilities limited, they can own guns, they can work, they can do just about everything everyone else can do, but not marry.
Incest is something that is known to harm babies who are produced from incest.
Polygamy is banned, however this is equal for all.
All individuals should be free to choose to marry whoever they like. The law states one person at a time, white people, women, black people and everyone else is limited to marrying one person. You can argue the toss over whether this should be like this or not, but it's FAIR for all. Banning gay marriage prevents individuals marrying a consenting adult of their choice.
But, from the LEGAL point of view and a CONSTITUTIONAL point of view (you remember the constitution?), the 14 amendment has an "equal protection of the laws" clause, ie, you can't stop individuals being able to have equal protection. Two consenting adults can marry who they choose and get all sorts of laws in their favor, tax breaks or whatever, gay people cannot. It goes against the constitution.
Important functions like marriage and driving? Are you kidding me and putting these two on the same level?
Actually, the US govt DOESN'T control all driving. You can drive on your own land how the hell you like, as long as you don't hurt someone. So can I marry who I like on my own land? er... no. Not if I were gay.
Now here's the really funny part.
"It has a right to exclude certain people from those functions in order to maintain their integrity"
Straight marriage has nigh on 50% divorce rate. Integrity? I think not.
Now you want marriage about best interests. I'm sorry, but when a couple gets married, the US govt, nor state govts, don't say "is this in the best interests of the state for you two to be married?"
Then you go and talk about POPULATION DECLINE. Oh my GOOOOOOOOOOOOOOD. (I hate that phrase but whatever).
7 BILLION people on the planet, TOO MANY. 300 million in the US, TOO many. And you're worried we won't be producing children enough.
And then you think if gay people don't marry they'll go marry a straight person, just to marry. Sorry, they'll still be shagging their same sex people.
You say the family nucleus will go into a free for all. Sorry, for a large part it's already there. 40% of first marriages end in divorce, plenty of kids are in single parent families, plenty of kids are in families with two parents (straight) which are abusive.
You think the barn door will open? Sorry, straight people kicked the damn thing open and broke it down in their rush for MONEY and MATERIAL ITEMS and CHEAP SEX. You know married people sometimes cheat on their partners and then get kicked out of the house? I saw it happen last week.