What's Wrong With "All Lives Matter"?

   Though I think that Black Lives Matter (the movement, not the slogan) is largely wrong about some of the crucial facts, I do think they have a point about "all lives matter." I mean, I think that "all lives matter" is largely true...not exactly true, though...because I don't think that, e.g., Hitler's life matters...but I know what they mean. It's pretty true.
   But I think that it's not great as a criticism of/response to "black lives matter" (the slogan). "Black lives matter" is roughly equivalent to "black lives matter too." So "all lives matter" kinda misses the point--though it's understandable that even well-intentioned people could miss that point, I suppose. So "black lives matter" is like:  "Look, we all know that white lives matter, right? That's not something anyone really disagrees about. It's not an issue that even comes up. But here's the thing: black lives also matter." Responding "all lives matter" seems to me to be a mistake given the proposition(s) actually being expressed. They're saying something like: black lives matter just as much as white lives matter. So that all seems pretty obvious to me.
   But anyway, my real point is: given that BLM believes (justifiably (though mostly falsely) believes) that there's an epidemic of cops killing black men, and that it's purely out of racism and/or disregard for their lives...well...  Imagine that Smith's wife has just died. Overcome by grief, Smith exclaims "I loved her so much!" Jones, standing nearby, responds something like "Well, we all love our wives..." I mean, it might very well be true...but Smith is a jackass of world-historical proportions for saying it just then. It's not that it's false, but that the pragmatics are out of whack. I mean like waaaaay out of whack. Not a terribly deft analogy, I'll admit...but something like that maybe?
   Rhetorically speaking, it might be good for the response to "all lives matter" to be something on the order of: Yes they do; if you believe that, then we're on the same side, my friend. But even if that might be more effective, the more important question is: is ire in the face of "all lives matter" as a response to "black lives matter" defensible? And it seems to me that it is.