Genesis 2:18 sets the stage for (one account of) Eve’s creation. God declares that “it is not good for the man to be alone,” which is why God decides to make, as the NRSV translates, a “helper suitable for him”: Eve.
Because Adam and Eve are the paradigmatic married couple in the Bible — and more generally, because we are all Adam and Eve — one interpretation of this arrangement in Genesis is that men should only marry women and women men.
Buttressing this claim is an often-cited alternative translation for the Hebrew word k’negdo. While the NRSV renders this as “suitable,” some others focus on the root of the word, neged, and translate the word as “opposite” or “complementing.” If so, Eve’s purpose was to be different than Adam. More generally, a man’s spouse is supposed to be different than him, that is, a woman.
As it happens, k’negdo doesn’t mean “different than him.” It means “matching.” One way to match things is pairing things that are opposite, but certainly it’s not the only way. In spite of this nuance, however, the complementarian interpretation of Genesis is reasonable.
But it’s not the only reasonable interpretation.
It’s just as reasonable to focus on the point of Eve’s creation, namely, that Adam shouldn’t be alone. More generally, people shouldn’t be alone. If it then turns out — as certainly seems to be the case — that some men can only find partnership with other men and that some women can only find partnership with other women, then Genesis 2 might not only allow homosexual marriage but, in fact, demand it.
In other words, one way of looking at Genesis 2 is that people should behave like Adam and Eve, a man marrying a woman and woman marrying a man. Another equally valid way is that people should behave like Adam and Eve, finding a partner so they are not alone.