What brand of fusible did you buy? Someone else posted recently about having the paper come off in tiny pieces when she first started. I will see if I can find that thread.
Edit: I found the reference, but it was to Printed Treasures:
Need help with Printed Treasures
and the followup:
Printed Treasures Wonderful Customer Service
Although it's possible you have some bad fusible (or old fusible), more commonly this problem comes from user error. When I have had difficulties removing the paper, reheating the fusible with an iron has always softened the fusible and made the paper removal easier. However, I suspect that if a too-hot iron is used and/or the fusible is heated for too long at high temperature, this also may make the paper hard to remove.
As was mentioned in one of the above threads, you can soften the paper with water and then rub it off. Or you might want to just leave the paper in and trust that it is going to disintegrate eventually in the wash. With my sister's quilt, the applique with the paper in was rustly and made noise, and was a little stiff, before I quilted through it. After quilting and washing it was much better, and after a couple of washings the paper could no longer be detected even though I knew where it was.