Why should I (or anyone) support BLM?

I don't understand the nature of the BLM movement. It appears inherently divisive, and there don't appear to be any consistent, solid arguments that they put forth. As far as I can tell, it's a highly decentralized movement that contains ideas ranging from egalitarianism to straight-up supremacy. BLM appears to be disorganized, but its existence still rests on some sort of moral outrage. In that regard, it is similar to the libertarian movement, or at least certain strains of it. Now, when I discuss a political topic, I construct a case using moral reasoning and a fair bit of evidence. When all the facts are in order in a discussion, you boil it down to principles, which is where you find ideological rifts. For example, a progressive and I might agree on the definition of anti-discrimination laws, but when we look at the morality (or lack thereof) behind them, we'll come to completely different conclusions. (We haven't forgotten about BLM. I'm getting there.) My goal in a discussion (most of them, anyways) is to present my case and defend it. Presumably the other person will do the same thing. [i]I[/i] argue [i]my[/i] case, and [i]I[/i] provide [i]my[/i] evidence. It's up to me to change the other person's mind, or to at least show that there's reasoning behind my position. I don't expect most people to drop their preconceptions and say, "Hey, those libertarians and voluntarists are on to something." It takes discussion to change minds. Right. So we come back to BLM. I don't expect people to happily and blindly support my movement. It wouldn't make sense for BLM to expect any differently. I understand that BLM supporters, apologists, or what-have-you aren't a majority here, but I'm sure there at least a few. Convince me (and by extension, others). [b]Why should people support BLM? If it truly isn't a divisive movement, then it would seek to gain support by presenting its case. I have yet to see that case.[/b]