Being in the unique position of being an Instructor at one Art School (for kids 2-18) and a student at Emily Carr university I see two major reasons for young people liking film. One, the hipsters/scenesters/lomography crowd. Their alternative life style revolves around vintage, so there is a large, and growing, popularity to shoot classic SLRs ect. My students, who range from 9-18, all love the process of the darkroom, and seeing their prints come to life.
For me, I enjoy the work flow of film. I also enjoy film cameras, they're much more enjoyable to use than my DSLR. I also shoot alot of medium and large format, a process that I can't copy digitally, and I dont have 40,000 dollars lying around to drop on a Hd3 or the like.
All that said, digital has its place. When I'm shooting jobs I rarely use film. The process of digital lends it self very nicely to most forms of professional photography.
Oh yeah, I'm 21, been shooting for 7 years.