IMO this all has to do with tradition. "Happy Holidays" was a phrase that received substantial amounts of negative press because people got upset when they were told they could no longer say "Christmas". Only in the last couple decades have people decided that Christmas should no longer be called Christmas...EVER.
This irks people. We are happy when people celebrate their heritage by saying things like "Happy Hannukkah" or "Eid Mubarak", but we tell people they must use "Happy Holidays" instead of "Merry Christmas".
That has never made sense to me.