I agree but as a society we really need to start using the English language better. Unfortunately, when you say something like "Black lives matter", the immediate reaction you have upon hearing that (if you are not black anyway), without even knowing what it is all about, is "Of course, but all lives matter." As others have suggested, a slogan like "Black Lives Matter Too" bypasses this sort of knee jerk involuntary reaction. But I suppose BLMT sounds more like a sandwich...
It reminds me a bit of "white privilege". I've always hated that term though it is hard to express why. I think this anecdote helps..at least a little: Someone I know made a post on facebook meant to illustrate how white privilege exists (he's white). When he was younger, he said a cop stopped him on the street because he fit the description of someone who had shoplifted, or vandalized something or had committed some other relatively minor crime. His response to the police officer was to complain that his rights were being violated, he was going to call the chief, etc. Anyway, at the end of the day there were no negative consequences for him. His point being that if he had been black, there's a better chance that unnecessary force would have been used against him.
However, to call this "white privilege" is terrible. The police should not be able to infringe on anyone's rights. Those rights aren't privileges for whites or anyone else. To speak of it that way implies that whites are being treated unfairly in a positive way...granted privileges that they should not have. That's not what's happening. They (in this example) were treated how they should be. The fact that others may not be is the problem that needs to be addressed. I tend to think that police brutality and the use of excessive force and other violations of rights by the police are the real problems. There may indeed be a racial component to that in many cases but it isn't exclusive by any means. Nobody should be treated like George Floyd.
Perhaps that isn't what is meant by those who coined or use the term but words have meaning and people tend to react to them based on their meaning, not what you intend. Martin Luther King was damned good at expressing these sorts of things. It's seems that few since are able to do a very good job of it.