There's nothing wrong with saying Happy Holidays.
People say Happy Holidays simply because Christians don't have the Monopoly over the month of December in terms of Holidays, and its the polite thing to do.
Kwanzaa, Haunakah, or Eid al-Adha anyone? (Wikipedia links)
People who get bent out of shape over this issue are mostly the Christian far right fanatics who zealously force their beliefs on others, especially during holidays (Easter, Christmas and others). And they only come off as Discriminatory while doing it too. A prime example of this is the website Standforchristmas.com, which gathers data on what retailers don't display with people view as the "Christmas Spirit" or "Values" that they claim make up American Culture and Life. Some of the comments people put on this website are simply inflammatory and rude, and in some cases would be grounds for a Libel case (Legal term for Defamation when in print.)
Normally I loath political correctness with an unbridled passion, but this I let slide, simply because I have friends of other faiths that simply don't celebrate Christmas, one of whom is Jewish and lives in Israel.
This is simply a "look at me, I'm more important" issue. People have a right to not be bombarded by something they don't believe in while at the same time be recognized for something that they do, even if its only a generic all encompassing phrase like "Happy Holidays".
Also, when it comes down too it, when you combine all the people who celebrate holidays other then Christmas in December, they outnumber those that do rather handily.
Now, if you'll excuse me, I'm going to go troll up some chaos on Standforchristmas.com...