The point of the BLM movement is that just because someone is black, the cops shouldn't just assume they're thugs and treat them accordingly - something which does happen...a lot.
But you're right when you say that they shouldn't choose black people who happen to be thugs as the examples for this campaign. It really doesn't help the cause. It actually does the opposite.
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I live in South Africa. We have it even worse than you guys when it comes to violent crime. You may have heard of Oscar Pistorius, the famous (now infamous) paralympic athlete who murdered his girlfriend by shooting her 4 times with hollowpoint ammunition while she was in the bathroom behind a closed door. He claimed that he thought she was a criminal and thus he was acting out of a legitimate fear of his life.
Luckily sanity has prevailed because his defense is bullshit and most sane and rational people know that in reality, people aren't living in this constant state of fear. As human beings we actually can't. Fear is an impulse response - it results when our situation changes. When the level of danger we live in is constant then we quickly adjust to that as the norm and continue with our lives. Obviously there are ways to keep a person in a constant state of fear, by continually changing the environment and introducing new stuff to be scared of, but being in this state for an extended period of time would surely result in insanity.