Like most people, I normally use digital photography for 'day to day' pictures. That's primarily because it's far cheaper. (Non-reusable film costs a great deal more than a reusable media card and their are no processing costs with digital). Further, it's far easier to manipulate images at a later stage.
However if I wanted to teach someone 'serious' photography, I'd always start them with using a film camera (possibly with a hand-held light meter). It's a much better way to get them to understand the concepts of shutter speeds, apertures, depth of field, lighting, etc. (Also, someone who's got to pay for film and processing is far more likely to take the time and trouble to correctly frame and expose a shot, than someone else who can shoot hundreds of digital pictures in the hope that few of them will turn out OK).
Also, if a friend or relative asked me to do some serious photographic work for them (e.g. wedding pictures or family portraits), I'd probably reach for a film camera. A 35mm SLR, equipped with a decent zoom lens, offers far better control over depth of field than any digital camera (within the same price bracket) could ever do.
Chris