(Ducking all the incoming downvotes - I'm keenly aware of how unpopular this position is, and how bigoted it seems to most folks these days - which sort of proves my point.)
The other possibility that you seem to implicitly dismiss is that the original reasoning is understood perfectly well, has been debated to death, and has been found to no longer align with what the majority of people want out of society.
Chesterton's Gate argues against removing the fence out of haste and ignorance, but not against removing it after intense debate and careful consideration.
Careful reconsideration? I don't see how that played any part of this recent shift.
- Lois McMaster Bujold, "A Civil Campaign"
We just happen to be living in a society that's in the middle of its way from point A to point B.
People kept trying to explain their reasoning against same-sex marriage but failed, which almost everyone sensible takes to mean that line of reasoning is now invalid. I never heard an argument against it that was even coherent, other than the pure theological command ones.
The line of reasoning I've heard is that intersex marriages produce families, which societies value.
Same-sex marriages do not produce children, as a simple result of biology. I don't deny that a same-sex marriage can form an effective family through adoption or surrogates, nor that an intersex marriage can fail to produce children, but the default result is children in intersex marriages and no children in same-sex marriages.
If society wants to encourage children and families (for obvious reasons), one simple route is to encourage intersex marriage. Same-sex marriage is, in this supposed society, 'discriminated against' because it doesn't produce the same result as intersex marriage, in the same way that you can't marry yourself, or 'donate' your income to buy a new car for yourself instead of to a charity and expect a tax break, or spend your retirement savings tax-free before retirement.
I also don't deny that this simple route of encouraging the raising of children by encouraging intersex marriage isn't perfect, and the imperfections cause harm. But it's kind of baked into our culture and legal system. Suggestions that simply extend the encouragement to same-sex marriages to eliminate the harm without fixing the encouragement are also incoherent, failing to see the reasoning for the fence. I wish you good luck if you want to take away the benefits from childless intersex marriages, or not extend them to childless same-sex marriages. And a lot of the noise around the issue is based on emotional, theological or incoherent reasoning, which makes sensible communication difficult.
That's a greatly over-simplified view of it; for a good chunk of history, European marriage patterns served to reduce or delay fertility. http://www.collective-action.info/_THE_MarriagePatterns_EMP
Consent as recent innovation: until horrifyingly recently (1986 in the UK, similar dates around the West), there was no legal concept of rape within marriage. Consent was a one-shot deal on your wedding day for the rest of your life. Going a bit further back, it was only in the mid-20th century that the law stopped supporting husbands from physically retrieving fleeing wives. Divorce - the withdrawal of consent from a domestic situation - is really a 20th century innovation. And back before the 20th century, wives could not own property. Marriage is already quite literally not what it used to be.
Following from contraception: the focus on marriage in history as the only legitimate form of sex was "about" prevention of children, not encouragement. Often achieved with considerable brutality towards women who produced children outside of marriage (Magdalene Laundries passim).
Marriage has changed in the 20th century as a recognition of the equal rights of women as individual human beings. It has further changed in the 21st as we recognize that homosexuality does not disqualify people from equal treatment as human beings either.