It contradicts reaility. The Supreme Court has established that marriage is a "fundamental right" under the United States Constitution.
Perhaps you have heard of the Due Process Clause, which prohbits local and state governments of denying life, liberty, or property, withut taking certain steps. Marriage is fundamentally about life, liberty, and property.
If you want to argue that "same sex marriage" is not a right, then that is one thing, but don't even try to argue that marriage in general is just some sort of privledge. That is neither historically, nor rationally corrrect.