Everyone is confusing Freezer PP with regular. you do not stitch through the paper with Freezer paper, you fold it back and stitch next to the fold. The beauty of the FPP method is not tearing and you can reuse the patter piece multiple times. Here is a link to FPP with pictures so those of you who comment that you use cheap computer paper, Carol Doaks, kids scribble pads can understand the difference..
http://www.twiddletails.com/store/in...age=page&id=21.
Regarding the OP's issue of fabric fraying when you pull away the paper. I have never had that happen more than a few threads. Try hitting it with your iron again before peeling. That should remelt the waxy coating enough to get it to release easily but you may sacrifice the amount of times you can reuse your pattern piece.