Well, always is kind of a dangerous word to use in this case, as I can think of many movies where alcoholic drinks are served in other containers, including proper cocktail glasses.
As for when the red cups are in use, they are simply a cheap and affordable way to serve drinks to large numbers of guests. Using them means not having to worry about things such as keeping a large number of real glass or crystal glasses in stock or the possibility of glasses being broken during the party. When you are finished, you can just throw them away instead of cleaning and storing them. They are also considerably more environmentally conscious than using white styrofoam cups, which are traditionally associated with hot drinks and coffee instead of alcohol.
The red color is really an arbitrary point. Many companies manufacture the glasses in this color, among others. In my own experience, I've actually seen more bright blue glasses in use at parties, including my own.