True, but... It also is stated specifically against cops AND some of it has caused a backlash against them in lost lives. Words do things. As much as I believe Black lives matter, I truly believe that Blue lives matter (and white for that matter).
While I sympathize.... the 'way' rather than the actual message was the problem behind this particular sentiment. In addition, there were a couple of other shootings by police in mistaken identity such that 'white lives matter too' is appropriate. In among the problem shootings, as this OP states, there were some lives that mattered, but were hazardously placed in harm's way by bad (illegal) choices.
I believe we've fostered a 'military' mindset in the police force in recent years. This in itself creates problems where 'protect and serve,' I think did a better job.
Inherently, anything that singles us out, however, can and does more often 'separate' and cause harder feelings. We've talked about this before. I've talked with 3 people of color (all kinds, not white) this week. All of them expressed a problem in the South so I realize we have separate realities. The black man next door to my mom was talking about the 'color' walls as nonexistent with my mother.
I've grown up trying to be colorblind so "BLM" is a bit against that attempt and actually causes a different kind of problem. I YET think 'colorblind' is the answer and that we proceed defending unjust causes case by case.
I watched a PBS show
Finding My Roots and was frustrated that people were dragged into 'slavery' history of their family members and then asked "How does that make you feel?" Some of this goes beyond 'what is hurting you' and goes into 'what you should be politically outraged about.'