and the resultant lack of understanding. Dealing with the mentally ill requires the exact opposite approach from how police are trained to deal with situations.
With normally perceiving people, you go in with an exaggerated show of force to convince the person that resistance is futile. It would work for you or I, who aren't going to battle five guys in SWAT regalia brandishing weapons. However, any show of power to most mentally ill people who have lost control only convinces them that they are in mortal danger and they will react as if in mortal danger. This causes them to ramp up aggression toward police because to them they are fighting for their lives. The cops then feel threatened and ineffective because what they have been trained to do isn't working, so then THEY react in fear. Unfortunately, the average cop has more lethality at her disposal than the average mentally ill person, so things go bad from there.
The average police isn't trying to go out and shoot people, but their training fails them at a time when they have a gun in their hands and two frightened people facing off. The way to stop police shooting is training and a community mental health 1st responder unit that is trained to deal with the mentally ill before the police with their guns, testosterone, and tactics geared toward the mentally well even arrive.
Incidentally, testostrone in a mental health emergency is like bringing gasoline to fight a fire. And I am not implying that any one gender is better or worse in this situation. It all depends on on the control one has of one's reactions.