The phrase "Black Lives Matter" is pretty divisive, right?
It's singling out the black race, giving it value. How could that not be divisive? No one racial group has more value than the other.
With that said, the movement would be better off being the "All Lives Matter" movement. That way, we could make sure that no one feels excluded from a movement that gives value.
The problem there is that by naming the movement "All Lives Matter," we're losing sight of the actual problem that the movement is supposed to be fixing.
Standard problem solving is where we define the problem, zeroing in on it, coming up with a solution and after going over the alternative solutions, execute the most viable one. When the problem is the devaluation of black lives, our solution is to label a movement with words of affirmation that say the opposite of what our society says, while also working to change the minds of those who seem to believe that black lives carry lesser value, or change the conditions that create those opinions. So, ignoring the usual argument, that "All Lives Matter" silences the voices of "Black Lives Matter," it's just bad problem solving. It's terribly naive to assume that no problem exists to zero in on.
Feminism gets the same kind of issues. Due to the focus on women and femininity, it's all too easy to believe that it's all about giving women more value than men. Of course, it's really zeroing in on the group whose value is clearly less than, and working to change that.
Superiority isn't the goal, it's to give women their God-given value: the same as men.
Typically the phrase "Egalitarian" comes up in discussions about feminism, but to suggest that feminists re-brand themselves as egalitarians as some sort of solution, you're taking away the step of problem solving that includes zeroing in on the problem. We've moved past the step of defining the problem. Don't take issue when the subject of the issues is clearly defined.
That's not to say that the ideas "All Lives Matter" and Egalitarian are bad in any way, but to propose them as renames for movements that are accurately named is foolish. To solve these problems, we have to focus on what is being devalued in the first place. Those ideas are great by themselves, but the specifically named movements (BLM, Feminism, etc) are made with the intent that the generalized ones (ALM, Egalitarian, etc) could be true and the social norm, but right now it's not and so if you really believe in the ideas of "All Lives Matter," Egalitarian, or whatever broad social justice standpoint, you'll have to get behind the targeted ones first to prove it. Otherwise, you're most certainly sounding like a hypocrite. The name is a crucial part of the process and to change that would be to change the focus.