I think the question is worded wrong..
I'm not offended by Happy Holidays during the holiday season since it's Christmas and New Years, and it gives a nod towards the traditionalists who follow the 12 days of Christmas.
I'm offended that others have latched their 'holidays' onto it because they feel intimidated or whatever about the majority enjoying their celebrations.
I suppose the counter to it is falling back to just Merry Christmas... But Happy Holidays doesn't usually tick me off unless it is on a sign listing any and all 'holidays.'
I think the key word in the poll question is "instead". There is nothing wrong with "Happy Holidays" by itself, but when it is used to the exclusion of "Merry Christmas" it is offensive.