Unfortunately, when you add severe mental health disorders into the mix you can't really follow this "logical implication" path you seem so hellbent on. Add to that the fact that we as a society tend to not treat these problems as an unfortunate disease (but treatable), and put down this part of our population as if they weren't humans too doesn't help either.
Yes, I too, like everyone else, have a trait that a many people would hate and if murder is legal, I would be dead already but I'm not so worry about it because fortunately murder is illegal and carry severe punishment. I understand its not perfect but at least significantly lower my concern.