Those of us who are Christians celebrate TWO holidays this season: Dec. 25 and Jan. 1.  So why is it wrong to wish someone well for BOTH of them by saying Happy Holidays? That even includes my Jewish friends when Channukah is around the same time. 
But if you are speaking to a Christian who does not observe Jan. 1 as a holiday, by all means, simply say Merry Christmas.

What a silly tempest in a teaspoon.