We are claiming that a marriage between two men or two women is not essentially different from a marriage between a man and a woman, and so we are asking for that same thing: marriage. E.g., "I paid you for a Porsche, so park that Yugo and go get me a fucking Porsche."

Yes, the law currently defines it a certain way. That is the whole reason why we are challenging that law; it is unreasonably discriminatory. It cannot serve as an authority on the argument when it is the very thing being challenged. Nor can the Bible serve as the authority, because to use it as such would be to establish religion in violation of the First Amendment. (Arguments from the Bible could be used, but it doesn't really present any convincing arguments.)

But so far gay marriage opponents have put out few arguments beyond the arbitrary and invalid, e.g., "Marriage is defined by us as between one man and one woman, therefore marriage is defined by all as between one man and one woman." And the additional arguments haven't been anymore convincing, hence why they keep coming back to the circular argument.