My mother is a sweet law-abiding citizen, always follows the rules. But cops make her supremely nervous, and she's terrified of going to jail (even though, like I said, she's done nothing wrong, but that doesn't always matter). I'm afraid she's gonna get pulled over for a broken tail light or something and end up getting hassled because she's "acting suspicious".

I would assume cops get training for dealing with people in stressful situations, but from all the instances of things going downhill so fast for little to no reason, it doesn't seem like the training is sufficient (or like you suggested, maybe they are taught the wrong things altogether). Their mere presence can make people anxious, and stress alone can cause people to have difficulty processing the situation (not to mention the conflicting orders, the dogs, the yelling, the flashing lights, etc). I know that, for the things I've been trained to do, it's a constant struggle to remember that others don't know even the basics of my field, and assuming that they do is a recipe for miscommunication. But when i communicate poorly, it doesn't end with people getting shot.