Well, the fire department does tell people that they need to pay attention to things that might cause fires. The response isn't "well, people should pay attention to all dangerous things! What about car accidents?"
I mean, this isn't a difficult concept to grasp. When someone is raising money for orphans, people don't usually say "but what about money for veterans?" When people are raising awareness about breast cancer, you don't usually tell them "hey, we should be raising awareness for all cancer." They don't get angry that Smokey Bear focuses on forest fires ("Oh, house fires don't matter to you?").
People understand single-issue campaigns for most things, but some suddenly have an issue with it when it comes to African Americans deaths. This naturally raises a few eyebrows.
The controversy isn't because it's a bad slogan. The controversy is evidence of it being the correct slogan.
It seems that the argument has been framed around black people's mistreatment in general, which is fair enough, but, when specifically talking about the police, it seems to me that getting the latter to be less trigger-happy would alleviate the problem for all races, which is why I find the focus on black people a bit odd.
A group of people is experiencing horrible and unjust treatment. The implication of the situation is they don't matter, and the correct reformist statement is that they do matter.
Black lives matter also is not the correct statement. It is the correct understanding of the while situation but you need to keep in mind the nuance of language.
I'm not really up-to-speed with US politics, but I know it's horrifying how easily and with impunity the police have been killing black people. Still, "Black lives matter" isn't a great slogan, and calling "all lives matter" racist definitely seems like an overreaction. I'm not familiar with ALM's positions, though, so maybe it's a racist organization in disguise, I don't know.