From an essay in Christianity Today:
The Jewish Hanukkah story is one of triumph over a culture that wanted to force the Jews to assimilate against their will. The Christian Hanukkah story is one that starts with Jesus asking provocative questions, but retreating rather than forcing the issue.
To insist that non-Christians say "Merry Christmas" instead of "Happy Holidays" runs against the lessons of both Hanukkah stories.