14th Amendment
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
--------------------------------------------------------
If it is legal for you to marry your sexual preference, it has to be legal for anyone to marry their sexual preference. It's called "equal protection" and it is outlined in the 14th Amendment. You see, currently, marriage is the union of a male and female of consenting age, that is the parameters we've established and adhere to, and everyone (including gays) has the right to do. If we alter the definition of marriage to include a sexual preference, then that becomes the parameter we codify into law, and we must adhere to the constitution regarding it, whether we like it or not. So when a goat fucker comes along and demands his right to marry his goat, because that is his sexual preference, then we have no basis on which to deny him this request, and we can't deny the request and remain true to the constitution.
Now, the goat fucker example is a little extreme (which is why you brought it up), most goat fuckers tend to keep that a secret and wouldn't likely emerge from the closet to demand their rights anytime soon, our generation would probably not have to deal with it, but eventually, someone would bring the case. The more likely scenario involves polygamists, who are already lobbying in states which have passed gay marriage. Again, the problem is, you can't say THIS sexual behavior is okay as a basis for marriage, but THAT sexual behavior is not. If you do say that, you are in violation of the 14th, if marriage has been defined by a sexual lifestyle, which "gay marriage" is, it's in the name!