It does sound to me like perhaps you are brushing harder then you need to. Even when Trev had like 4 or 5 inches of hair on his neck and legs and at least 1" everwhere else I never got very much loose hair out when brushing. A little bit, yes, but certainly not a handful! It sounds to me like you are breaking the hairs off, especially considering that you say he's 2" long and doesn't have as nice of a coat. I would go with what everyone else is saying, use a spray-on conditioner and part the hair as you brush. Also, try using a "pat pull" motion instead of a "dragging" motion. Bring the brush down in a patting motion (using the full pad) and then pull slightly down and away. Almost like you are drawing loops going away from your body with the brush. Does that make any sense at all? Lol...it's much easier to show someone then to describe it.

If you just drag the brush across the hair, then yes it pulls on the skin and hair, which is uncomfortable for the dog and breaks off the hairs. And when brushing out a mat, start at the tip of the mat and work inward, just like you would when brushing your own hair. Those mats come out sooo much easier when you combine starting at the tip of the mat and the pat pull brushing motion. Most dogs don't even mind me brushing them when I do that.
And don't force a comb through the coat...chances are, if you have to force the comb through, you missed mats. What I do, is brush the dog until I think I'm done, then I take a comb and go back over everywhere. If I can't slide the comb through easily in a certain area, then I go back at that spot with a brush. On some poodles with very thick coats, getting a comb through (even on a mat free dog) is very difficult. Try using a wider toothed comb, that should help.