No, this is incorrect. If you truly believe that marriage is a vehicle for procreation and the government has a valid interest in it for this purpose, then all unions which cannot procreate would not be valid. This includes heterosexual couples who are infertile or who do not want children.
Just because the two are connected does not mean that there is not a massive and important difference between procreation and
raising children. Infertile couples and couples with inheritable genetic disorders, much like homosexual couples, are more than capable of raising children they have acquired by other means.
My opposition to incestuous unions is not based on genetics, and I do not believe that the laws which prohibit them should be based on genetics, either-- unfortunately, the laws and the majority of the populace disagree with me on this issue, just as they seem to disagree with me on nearly every issue pertaining to family relationships.
In any case, it is not necessary for the institution to only promote those relationships which provide a healthy environment for children, only to promote those relationships which
tend to. The fact that intentionally childless couples can be married does not detract from marriage being the best condition in which to raise children, and thus does not detract from the government having a legitimate interest in promoting marriage.
Lastly, government's interest in marriage is not merely over procreation.
What would you say that the government's interest in marriage is, then? For what other reason should the government subsidize and extend special privileges to certain kinds of relationships between adults?
After all, in order to argue that homosexuals should be allowed, we have to accept the point that heterosexual marriage is a valid social institution and that the government has a legitimate reason to encourage it. As much as I am vehemently opposed to the position, several people have stepped forward and claimed that the government has no business in marriage whatsoever.
I can defend marriage-- whether it is equal opportunity or not-- on the grounds of providing the healthiest and most stable home environment for children. I can probably defend it on a few other grounds, though my argument will be shakier. I think anyone would be hard pressed to defend marriage on no grounds whatsoever, and that appears to be all you're offering to counter mine and Jerry's position.
Put simply: if you value the institution of marriage in terms of what it means for families, then you should have no problem with new people entering that institution in the name of their families. That is exactly what the pro-GM movement is about at its core.
I would argue that depends entirely on the nature of those new people. I support extending marriage benefits to homosexual and polygamous unions, but I am strongly opposed to lifting any of the other legal restrictions on marriage-- and there are several additional restrictions I would like to
impose on whom may get married, and especially on whom may get divorced. I would like those States which allow first cousins to marry to cease, and I would like to see marriages to prisoners and foreigners more strictly controlled.
In fact, I've proposed as a potential compromise that homosexual marriages be allowed to marry as long as everyone-- homosexual and heterosexual alike-- is married under the terms of Covenant marriage or something similar. Sadly, noone else has taken me up on the offer, and I'm a little confused as to how people can be so opposed to homosexual marriage and still so accepting of casual no-fault divorce.