The black hole death problem

I think your first explanation of how hawking-radiation works (which you called misleading) doesn't seem very logical either. You could argue that the "+" particle always falls in the blackhole and the "-" article escapes. That would mean the blackhole is growing very slowly. Or , what i think would happen, both is happening at the same rate and has no relevant effect at all. For me, this concept of how the black hole evaporates slowly doesn't make sense. Can anyone explain it?