I'll take that bait.
No flaw in the logic itself. It does, however, bear NO connection to the question at hand, in other words, the proverbial red herrring, something thrown out to make us think about something else, instead of the question in front of us.
What the X in Xmas means to the individuals who use it has not been the point of discussion. The discussion has been about the origins of its usage, and it would appear that Christians for quite a long time have used this shorthand.
We'll note that you don't approve, though.
There is a bit of irony in your comments, already pointed out by another, of you using an abbreviation for Christ in your FR handle.