Modern transmissions are so well synchronized that you really don't need the clutch while shifting up or down, if you use proper technique and timing. I think there's a bit more shock to the parts on downshifts, and I like to control the back torque when shifting down, which is why I use the clutch then. On upshifts, there really isn't any shock to the parts that you don't have when using the clutch, provided you're off the throttle and in the right rev range when you do it.
Why do it? I don't have a good explanation for that. It might just be sheer laziness, or the desire to save the hand a bit when in situations where you need a lot of shifting. One advantage is that you can pick your nose while accelerating. Oh wait, gloves...