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Sorry, this applies on both ends. One of his key assertions was that the Constitution does not define marriage. Even as the 14th Amendment grants equal protection under the law, it doesn't define marriage. So, how can people ask for equality under a premise that doesn't exist in the Constitution? The law itself does not define marriage.
The law itself does discriminate against gays and lesbians, denying them a fundamental right. If the State is going to deny rights, it needs a good reason. And in the case of gay marriage it doesn't have one. It has no rational reason, nor does the denial serve any compelling state interest. It discriminates....because it can. That's insufficient to deny a right.
The Loving decision demonstrates, undeniably, that the federal government has the authority to rule on state marriage laws that are unconstitutionally discriminatory. Your entire premise, that the federal government needs to be able to define marriage into order to rule, is false. The courts need only have the authority to protect fundamental rights to rule. The burden is on the State to provide a valid justification for the denial of those rights.
And no such justification exists.