(1) People have a lot of misconceptions about ancient Greece. It was neither a gay utopia nor some homophobic theocracy. It was a society which, like ours, struggled with and debated over all sorts of social issues, including homosexuality. In fact, it was multiple societies spread out over multiple polities with different sets of laws (all of which evolved over time). So while there is a tendency to think of ancient Greece as if it were just Athens (or to superimpose Athenian culture onto Greek culture at large, with the possible exception of Sparta), that is an overly reductive way of thinking about things.
(2) While marriage was a legal/political institution in some ancient Greek polities, it was a private/social institution in others. Athens didn’t sanction any marriages, regardless of whether those involved were of different sexes or the same sex. Sparta had legally recognized marriages, but they also mandated marriage and punished people for not having children. Neither system really works as a model for US law, not least because the place of marriage in society has changed so much over time.
(3) Common to most ancient Greek societies was a distinction between marriage as a domestic contract and relationships as a source of romantic and sexual fulfillment. Indeed, romantic and sexual relationships were often seen as something to be pursued separate from marriage. It is in this context that we see praise for same-sex relationships in ancient Greece. But as the modern conception of marriage has moved away from mere domestic partnership and emphasized the role of romantic and sexual fulfillment, we have had to accommodate into one institution what used to be considered separate (though not necessarily mutually exclusive) functions.
(4) There were same-sex unions in ancient Greece (as well as most other ancient cultures). Again, marriage was a social institution in many ancient Greek polities with varying levels of ceremony and ritual surrounding it. In such societies, people of the same-sex could get married even if most of their fellow citizens disapproved of it so long as they were capable of enacting whatever ceremony was culturally required. This wasn’t possible in all polities, of course, but it was possible in some of them.
(5) Social approval has never been the test for whether a marriage is legitimate in the US. Plenty of people disapprove of interracial marriages. Plenty of parents disapprove of their child’s spouse. And celebrity marriages are subjected to all sorts of scrutiny, much of it disapproving. But that doesn’t constitute a reason for not recognizing those marriages. In Loving v. Virginia (1967), the US Supreme Court declared marriage to be “one of the ‘basic civil rights of man,’ fundamental to our very existence and survival.” Once that declaration was made, state recognition of same-sex marriages in the US was more or less inevitable. And the Loving decision was, in fact, cited by the majority opinion in Obergefell v. Hodges (2015).
(6) It does not follow from “same-sex relationships were sanctioned but same-sex marriages were not” that “prejudice wasn’t the reason for the exclusion.” If one institution is held in higher esteem than the other, then a prejudiced person might believe that some people are only “good enough” for the lesser of the two institutions. This isn’t to say that such prejudices were in play in ancient Greece. To the extent that there was exclusion, it was more about the perceived function of marriage than its status (and again, the perceived function of marriage has changed over time). The point is just that the one does not logically follow from the other.
(7) Plato became increasingly homophobic over time, as evidenced by the differences in his early, middle, and late writings. And in any case, Plato was skeptical of sexuality in general. He was suspicious of all things physical, after all, and he viewed heterosexual sex as an unfortunate prerequisite for procreation. If we truly decided to take him as our guide, we would create children solely through in vitro fertilization using gametes from only the most elite members of society and exterminate anyone born in a different way.