Die Hard is Chistmas movie started off as tongue-in-cheek comment, but over time, hearing it again & again, it evolved into more & more people talking themselves into it actually being a Christmas movie. But, would a true Christmas movie even start off as tongue-in-cheek?
Die Hard is set during Christmas Eve, but does the time of setting warrant it being a Christmas movie ? The main part of a movie is the plot? Is Christmas a necessity for the plot? I don't think so. You could set the plot in a different time of year & still be able to do the same plot with minor changes. In a story, it's not necessary for it to be Christmas for a man to travel to unite with his estranged wife & kids, it's not necessary for it to be Christmas for "Who said we were terrorist?" to take hostages & attempt to rob a building's vault. Does Christmas play any role in helping the protagonist, John McClane achieve his goals or does it pose an obstacle for him to overcome? No. McClane is not trying to rescue his wife & others, because it's Christmas. "Oh boy, I have felt the Christmas spirit so therefore I will attempt to save my wife!" Christmas is just the backdrop, not significant to the plot.
Die Hard was released in July, I've always seen it as a summer action flick first before a Christmas one. I guess it's more of a Christmas in July type of film to me. But, it is very appropriate to watch it during Christmas time, since it does take place during Christmas. However, a movie appropriate to watch during Christmas & a Christmas movie are not the same. Die Hard one of the most popular action films of all time that I see as an around-the-year movie, but people want to limit it to Christmas. When you say a Christmas movie, it seems to imply a movie one would watch only at Christmas time. I wonder if some people think it's a Christmas movie because they want it to be a Christmas movie?
Is the Christmas aspects of Die Hard even the reason most people love the movie? I think people would still love the movie without the Christmas aspects. When people say it's their favorite Christmas movie, I think they like it better than any movie that is about Christmas or set at Christmas time, but it's not because of the Christmas aspects, they merely watch it at Christmas time, because it is set at Christmas time; however they'll watch it other times of the year too, because again it's not really about the Christmas aspects.