Die Hard is a Christmas Movie for the following reasons.
1: The entire duration of the film takes place on Christmas Eve. If only a scene or two took place on/near Christmas, there would be more reason to discredit it, but the entire film takes place on Christmas Eve, which is a trait pretty much only held by Christmas movies.
2: There are multiple lines of dialogue in the film that reference Christmas or Christmas traditions ("Now I have a machine gun, ho ho ho"/"It's Christmas, Theo, it's the time of miracles, so be of good cheer"/"Alright guys, listen up, Twas the Night Before Christmas and all through the house..."/"If this is their idea of Christmas, I gotta be here for New Year's" etc)
3: The soundtrack of the film is almost entirely Christmas music. "Winter Wonderland," "Let It Snow," "Christmas in Hollis," and "Jingle Bells" are all featured, plus "Ode to Joy" which may not be exactly a Christmas song, but wouldn't be out of place in a Christmas movie.
4: Much like Santa Claus faces the impossible task of making all the children of the world happy in just one night, John McClane faces the impossible task of making all the employees of Nakatomi Plaza happy in just one night by saving their lives.
5: Home Alone is a Christmas movie and has the PG plot of Die Hard. One person outmatched by a number of criminals uses his superior intellect and surroundings to outsmart the criminals on Christmas Eve, all the while taunting the criminals using references while they fall into the traps laid by our hero.
