"Black lives matter" was a bad choice for a name, because it will automatically create the reaction "all lives matter", whether it's well-meaning or not. That creates a negative reaction right back. A name that was race neutral, or pointed to an objective goal like body cameras or having agencies outside the local police department/prosecutors to investigate police violence wouldn't have created that problem. "BLM" sets up a needless "us vs them" mentality.
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As far as the college protests, it's because they've been teaching a bunch of postmodern deconstruction and critical race theory, and they're teaching it as if it actually means something. Postmodern deconstruction is where you take something (the "text", it doesn't have to be literally text, it can be a movie, a game, real life, etc.), decide in advance whatever conclusion you want to have, and then take little bits and pieces out of context to support that conclusion. It means you can make anything say anything by taking pieces of the original text out of context, applying metaphors to make one thing mean something else, and so on. It's like playing the Kevin Bacon 6 degrees of separation game, going from one thing to the other in the least amount of steps possible. The technique is meant to just talk about the conclusion, and doesn't say anything meaningful about the original text(The student protesters/sjws miss this part for whatever reason). Anita Sarkeesian's videos do this (Bits and pieces of games are used not to talk about games, but about feminism. Only about feminism.). Critical race theory is doing the same thing with race.
So imagine a bunch of students taking this literally with every single aspect of their life. They're actively looking for racism, and they will find it. There's no way they won't, because that's the conclusion they're looking for. And then they try to get people fired who don't fix it fast enough, or use the wrong wording in an email. It's why a shit swastika, or some random idiot yelling a drive-by racial slur, or an email about halloween costumes can somehow become a Big Fucking Deal. Universities have hoisted themselves by their own petards by teaching this stuff as if it actually means something.