Is Demanding Separate Acknowledgement of Black Lives Part of the Problem?

I keep hearing from people that we must say "Black Lives Matter," and that "All Lives Matter" is an affront to the suffering that black people currently live under in Western nations, but I find this view baffling.

I mean it seems to me that we are safest if EVERYONE understands that they can be a victim of aggressive over-policing because after all, if I believe that an injustice carried out against another person could happen to me, it makes me that much more likely to oppose it as if it was an infraction committed against me.

If however abuses carried out against people that look like me are ignored by the media, as they often are, and activists are highlighting the abuses carried out against people who don't look like me and demanding that I acknowledge that the lives of people who don't look like me matter, how can it be anything other than a superficial virtue signal that will ultimately fail to either create long lasting change, or will make things worse if I begin to notice that people who do look like me are being attacked by the activists?

"Black Lives Matter" says nothing about the lives of non-black people, whereas "All Lives Matter" includes black lives.  How is it not better to acknowledge that All Lives Matter?