When my birthday arrives, I will not wish you a Happy Birthday, because I know that just because the day is important to me, it is not necessarily important to you.
If your intention is mainly to talk about yourself, go ahead with "Merry Christmas." If your goal is not purely self-absorbed, then you might want to take into account the fact that I'm not Christian.
If want to wish something for me, "Happy Chanukah" is more appropriate. I will not be having a "Merry Christmas" regardless of what you say, but I will be celebrating Chanukah and appreciate the good wishes.
But, I like to share the general happiness and really do wish well for other people, so I don't walk around saying "Happy Chanukah" to everyone. I know that's not meaningful to many people. I say Happy Holidays because that applies to everyone who wants to celebrate this month and I want to offer them good wishes in a way that takes their needs into account.