I care because Christmas is a legally prescribed holiday. When Channukah, Kwanzaa, or Arbor Day achieve that status you can re-ask me this question.
If Channukah were in August, and people started saying to you "Happy Holiday" wouldn't you consider it odd? "Why don't they call it by its proper name?" you might ask.
Further, if Channukah were a legal holiday of the Federal Government don't you think the above would be doubly curious? We have ten federal holidays, and in my experience they are ALL called by their proper names. Thanksgiving is Thanksgiving. Memorial Day is Memorial Day. Veterans Day is Veterans Day. So, why has Christmas Day morphed to "Holiday"?
Well, the answer is clear: a small minority of people who enjoy all the benefits of Christmas (like a day off from work, and an economy where 70% of the year's purchases are made in the "Christmas" season) want to deny the great majority of people in this country who both respect the legal and religious significance of December 25th their rights to linguistic freedom, and their rights to make this important legal holiday and religios holy day an important part of their culture.
Again, you can't force people to agree with you. Just go ahead and say whatever you want to say. When people start getting angry, as they did here in San Diego, things will change, but only in certain parts of the Country.