When you tear the surface of drywall, those fuzzy little hairs just keep coming through coat after coat of paint. The reason is that each time you sand it, they simply lie down and stand back up when they get wet with more paint.
The way to cure it from the start is to put a coat of shellac over the damaged paper. That will stand all the fuzz up but freeze it there. When you sand it off, they are gone and the paint goes on smoothly.
In the Learning Curve tab above there is a whole series of videos on working with drywall, including one specifically on this question: Drywall Repairs / Control Paper Fuzz.