Just say whatever you want to say. The whole point of the holiday in the West seems to be something to lift people's spirits in the face of a depressingly shitty time of year. Our part of the world gets bone-chillingly cold and even the trees say, "Fuck it, I'm out." Everything is dead and it's so cold a person can literally die from just standing outside for too long. Every other animal with any sense just goes into hibernation and sleeps past this absolutely shit time of year. Instead, we created this holiday to help get us through this "most wonderful time of the year" and we have to constantly pump out happy cheery Christmas tunes to remind ourselves what a great time of year it is, but deep down we all know, Christmas and Winter fucking sucks.
That's the point of the meme. I generally try to tailor my season's greetings to the person I'm talking to, if I can tell they might have a preference. Someone standing in front of me with a Jesus is the reason for the season sweatshirt on? Probably gonna get "Merry Christmas". The goth kid that was in line in front of them? Probably getting "Happy Holidays".
Would the goth kid complain to my boss about what I say to the other person? Almost certainly not. Will the "Christmas" person complain because they overheard someone say "Happy Holidays"? It's quite likely. Do I care what either of them say to me? Nope.
That's the thing. We'd like to be able to say whatever seems right, but for some fucking reason, "some people" get up in arms and pretend like they can't say "Merry Christmas" when literally no one cares what greeting you use, except the same people complaining about what they "can't say".
Also, sidenote: the venn diagram for people who complain that they can't say "Merry Christmas" and the people who intentionally misgender people is damn near a perfect circle.
It's a victimization fetish, which is probably why they're such a reliably consistent voting group, because they can be whipped up into a frenzy over anything and are constantly made to feel like their way of life is under attack. That entire world view uses that as justification for anything they do, since they're already "under attack", that completely excuses any trash thing that they do because they "didn't start it". They can never do anything wrong because everybody else already did something wrong first (whataboutism).
Reminds me, there was a study done with brain scans to see if there was a difference between liberal and conservative brains. Conservatives have larger amygdalas on average, so makes sense that their fight or flight reactions are higher.
I won't be surprised if besides that made up thing was created as a populist political point (I'd let you keep it, now vote), it could be also created as a marketing one (buy our xmas\alt-xmas merch to show 'em, btw we sell both). And that it's probably came as a part of the red scare, in spite of commies having long-going traditions around the New Year celebrations, some even more noticeable like statesmen adressing the nation at 00:00.
In some sense, it was the better part of the year because in agrarian society you just can't work at winter, can't plant or reap. You mostly chill and eat through what you have prepared before. If you didn't, well, you are fucked.
It's not that way with those who don't have a real winter at all (and that's where we all originally came from) and where some form of winter is all year round (where we started to settle not that long ago for whatever reason).
But in the middle of these two extremes winter is alike to that hibernation. It's a season you normally do 10% of your regular workload if everything is fine, because operating like usual is impossible. You also limit your consumption of fuel and food because you can't restore them without going out of your way. So making a feast from a limited supply does make sense, I guess?
If it's not your first winter tho, you'd be fine, and it's your time to socialize, to imagine stories and games, to love, to drink booze, to smoke, and to invent these celebrations because winter is fucking boring otherwise. As long as you reach over the line of a probable extinction - being an experienced prepper - you'd take five winters over one summer when you get exhausted and burnt out on a daily basis.