" ...because we are as scared of you as you claim to be of us."
But again (sorry for sounding unfeeling, I do understand), that's kind of on the police to get over that hump.
The public are afraid of inaction, corruption or at worst violence from those that should be duty bound, not to say decent enough, to be the opposite of that.
There are valid reasons for this because as we have seen, more officers have been shown to be corrupt or violent.
From your side you face all that the criminal element can throw at you whilst dealing with the vocal dissatisfaction being voiced by the non-criminal Joe and Jane public. Sometimes you are attacked and that is unacceptable and should be dealt with within the law.
However the difference is that you have a national organisation behind you, you are better equipped than the unhappy public (note not talking about the criminals here), have access to back up, and have the law on your side.
The balance of power swings heavily in your direction. The public have been, and are continuing to be failed until things within the system are fixed, so the anger will continue. So the metaphorical ball is and should be in your court. You are in a good position to help make the change for the better, but you need to take a step back, not take it so personally, and accept that there is value in what the public is saying - you (royal you) need to stop discounting things because they are couched in angry words.
People have a right to be angry.