Veterans Day is a federal holiday to honor people who have served in the United States Armed Forces.
It’s not spelled Veteran’s Day, because it doesn’t honor one veteran.
It’s also not spelled Veterans’ Day, even though it honors all veterans, because the Department of Defense says so.
More specifically, Veterans Day doesn’t belong to any one veteran, or any group of veterans. The word “veterans” is not assigned ownership, so it doesn’t need an apostrophe of any kind.
Grammatically, it might help to think of Veterans Day the same way you go to a Farmers Market, belong to a Homeowners Association or watch a Cubs game. Those don’t have apostrophes, either.