So now "between and man and a woman" is now "men paired with women." Even you can see those aren't the same thing.
But read up on it. You'll find that there have been Western institutions of pairing a man with multiple women. There have been institutions of pairbonding of men (specifically monks). There have been institutions of spouse ownership. You only have to go back a short way to find that the "traditional marriage" is a fairly recent invention. Again, read Coontz (yes, I know you won't, but she has a hell of a lot more documentation than I'm going to post here).
And hey, if we're going for "tradition," why not go whole-hog? Let's bring in all of the possible traditions. Widows must marry their brothers-in-law. Adulterers must be killed. Anyone who disgraces the family honor must be stoned. These are marriage traditions that go back thousands of years too.