Because everything else is exclusionary, including Chrismahanakwanzasolstiyulmanay which also has too many syllables.
WHOC stands for Winter Holiday(ies) Of Choice. I think I'm one of the people who coined it, circa 1997. It was a joint venture, at any rate. And I'm trying to get it to stick because I think it solves a lot of problems. It solves the problems of people who celebrate one or more Winter Holidays that may or may not be the most common or expected ones. It solves the problems of those who celebrate one Winter Holiday but associate with those who celebrate a different one. It solves the problem of not knowing what Winter Holiday another person celebrates, and so not wanting to say the wrong thing. The only real problem I see remaining unsolved is that of people who celebrate no Winter Holidays at all and I'm open to suggestions on this one. This isn't a problem I've personally encountered.
WHOC encompasses the Winter Holiday Season, which runs at least from the day after Thanksgiving (US) through Twelfth Night, and I'm considering an extension through Chinese New Year and/or Imbolc/Candlemas/Groundhog's Day. I could also be persuaded to start it early enough to include Diwali
WHOC-friendly greetings include "Happy Holidays" or "Happy Winter Holiday." Gifts can be given labeled "Happy WHOC." One can say "I'm going WHOC shopping" or just "Winter Holiday Shopping." Time off from school is for Winter Holiday Break or just Winter Break. We call the others Fall, Spring and Summer Break, after all. Greetings like "Merry Christmas" can and often should be given to those who are known to celebrate Christmas. Similarly, "Happy Hanakuah," "Happy Solstice" and "Happy New Year." I guess my point is that one should either know someone well enough to know her/his WHOC, or just give the generic greeting or gift.
For the record, my WHOC is Hogmanay.
Less important is what it ( isn't, and why. )
Happy WHOC, whatever you C!