When a law contains exceptions based on gender, such as your formulation, “Men are allowed to marry the opposite sex. Women are allowed to marry the opposite sex,” it is no different from older laws that made exceptions based on race, such as “Black people are allowed to marry the same race. White people are allowed to marry the same race.” Many Christian faiths (where our “primary definition” of marriage comes from) still insist that marriage should be retained between two people of the same church: “Catholics are allowed to marry Catholics.” The last time I checked, our government was supposed to promote religious freedom, which also applies to gay marriage.
What, in your opinion, is the reason governments sanction marriages?
Since marriage is fundamentally a religion-based practice, why would the government get involved in something that is, on the surface, none of their business?
1. Name me a U.S. state where that is a requirement, or has been any time in the last 200 years.
2. Name me any major religion that allows homosexual marriage in its core, orthodox teachings.
BTW, you are confounding two things here. It is and has been the rule of the Catholic Church that Catholics are to marry Catholics. That's true. However, that is part of the law of the Church, not the Natural Law. You can tell that because the Church can and does grant dispensations for Catholics to marry non-Catholics. Also, the Church recognizes the marriages of any two Christians to be sacramentally valid, and marriages between two pagans to be valid as well (though not sacramental).
But you absolutely cannot get a dispensation from the Catholic Church to marry someone of the same sex. Because that violates not just Church law which only pertains to Catholics, but also the Natural Law which pertains to everyone.
And on the interracial argument, the Catholic Church and I dare say most Protestant denominations never ever recognized the legitimacy of any American law that prohibited interracial marriage. Period. That was done by the state. Bans on interracial marriage never had any basis whatsoever in Natural Law and were therefore completely illegitimate from the date of their promulgation.