Let's take a step back.
Here’s the gist of South Carolina’s fascinatingly sexist argument. The state wants to prove that the 14th Amendment—which guarantees “equal protection of the laws” to every “person”—was not intended to displace state marriage laws. And what did those laws look like at the time? One major feature: In many states, married women were not permitted to own property or enter into contracts and had no legal existence apart from their husbands. According to South Carolina, the framers of the 14th Amendment explicitly preserved the rights of states to deprive married women of the ability to function independently from her husband. This right to deprive married women of basic liberties, South Carolina argues, is enshrined in the 10thAmendment and is not at all undercut by the 14th Amendment’s guarantee of equality.
The crux of South Carolina’s brief, then, is this: If the 14th Amendment permits discrimination against married women, it surely also allows discrimination against gay people who wish to wed. In fact, according to South Carolina, the 14th Amendment forbids only racial discrimination, leaving states free to disadvantage women and gays in any way they wish.
South Carolina's official position is that the 14th Amendment only applies to race, so women and LGBTQ Americans are not subject to being treated as human beings. The Equal Protection clause does not apply to them in any way, because at the time the 14th Amendment was written, women had fewer rights then men did (like voting).
This is the argument the state is giving to the Supreme Court in order to stop same-sex marriage.
That's astounding. It ignores a good 100 years plus of legal precedent, not to mention makes the argument that the 10th Amendment gives states the power to discriminate legally against women and gays and lesbians and a host of other people. It's incompatible with our society as a whole and I can't even imagine Scalia buying this argument.
But that's where South Carolina is.