No Natural Right to Gay Marriage

First off, I wholly support gays being allowed to married for multiple reasons.  However, I've been wondering if arguing that they have a natural right to be able to marry is actually true.  

The problem I see is that in order to have a natural right to get married, it would mean that we would have a natural right to something"unnatural".  

I don't mean unnatural in the sense that homosexual attractions are unnatural, because I don't think such attractions are unnatural, and even if they were, I don't think that just because something is unnatural it means it's bad or should not be done.  

What I mean by unnatural is that if humans (or some other species) had not created the instituition of marriage, it would not exist in nature.  And keep in mind that it is not just gay marriage that would not exist, but any kind of marriage.  So this argument would work equally well against a heterosexual couple arguing that they have a natural right to marry each other, but I've just chosen to focus on gay marriage because I never really hear people arguing that heterosexuals have the right to a heterosexual marriage (they believe it I'm sure, but they just assume it is true and never argue for it in the way the GLBT community has to argue for the right to gay marriage). 

Perhaps here one would want to criticize my argument saying that we obviously have lots of natural rights to unnatural, human-created things.  For instance, pop-tarts, like marriage, are human-created things.  However, one obviously has a natural right not to, for example, have one's pop-tarts stolen.  And this means that one can have natural rights to human-created things.  So just because marriage is human-created, it doesn't mean that we can't have a natural right to marriage anymore than we can't have a natural right not to have our pop-tarts stolen.

However, this criticism seems like it can be responded to by saying that the reason we have a natural right not to have the human-created pop-tart stolen is because of a much more general natural right: the natural right not to have our property stolen, and it just so happens that human-created things like pop-tarts can fall under the category of our property.

It is possible that we could have the right to marriage under a similar general right, but I'm not sure what this general right would be.  Is it that we have a natural right to create and be a part of any group or union we create?  Is it that we have a natural right not to be given different legal rights based on sexual orientation, so that if heterosexuals are given the legal right to marry, gays have the natural right not to be denied the legal right to marry?  Maybe it's that people have the natural right to pursue happiness, and for some this means being able to have a gay marriage, but I think that might be a bit of a stretch and one might think that people should have the right to marry who they will, whether or not it is in the pursuit of happiness (ex. a man gets a woman pregnant and while both the man and woman think they won't live as happy of lives by getting married, they want to get married anyway out of a sense of duty and obligation).

But maybe there is a general, natural right that I have not considered that would give people the right to marry.  I'm not sure.

In any case, I should be clear that even if people do not have a right to marriage, this does not mean no one (gay or otherwise) should be allowed to marry.  It just means that we would need other reasons for arguing that people should be allowed to get married other than having a right to marriage.  And seeing as how many of these reasons have already been voiced, it would not be so terrible to stop trying to defend the seemingly bad argument of having a right to marriage.