an amendment outlawing divorce? Or making it illegal for sterile people to marry?

The difference is that your amendments are hypothetical, while the 14th Amendment is the law.

Consistent with the amendment’s history, the Supreme Court has consistently held that laws can make make distinctions on the basis of sex, where such distinctions based on race or religion would be clearly unconstitutional.

Prohibiting a white man from marrying a black woman, when a black man is allowed to do so, is racial discrimination against white men, a legal distinction between races prohibited by the 14th Amendment.

Similarly, prohibiting a woman from marrying a woman, when a man is allowed to do so, is sex discrimination against women. The Constitutional difference is that the 14th Amendment allows some discrimination on the basis of sex where there is some plausibly arguable basis for the legal distinction. It doesn’t require that the Court agree with the prudential judgment supporting the law, only that it have some relation to the biological differences between the sexes, e.g. reproduction.

If the Equal Rights [between sexes] Amendment had been ratified, then it would be a whole different story and the sex discrimination against same sex marriage would be unconstitutional; but it was not ratified.

Full faith and credit for some state’s marriage between two women or two men is only relevant in another jurisdiction, if that jurisdiction has a legal institution that includes such contractual relationships in its definition. Because most states have no such legal institution, they have nothing where granting "full faith and credit" to same sex marriages in other states would have any relevance.

The federal government’s definition of marriage between one man and one woman only applies where it dishes out costs or benefits (e.g. higher taxes if married for couples where both earn good incomes; lower taxes if married for couples where one has low earnings). That does nothing to prevent a state from imposing costs or benefits on same sex couples it recognizes as married, so Massachusetts’ states rights argument is groundless unless its "sovereignty" includes overriding the federal government’s own right to define marriage for purposes of federal law.

Legal recognition of same sex marriage is inevitable, as opponents die of old age and supporters reach voting age. Still there’s no constitutional requirement that the federal government recognize same sex marriage before there’s majority support for it. When it’s enacted, it should be through democratic self government, not by judicial literary license.

same argument but never answers counter argument