I saw a similar explanation posted elsewhere, and it made sense to me:
I walk into a family dinner, where everyone is already eating. I can't reach any of the serving platters, so I say "I'd like some food". My family members turn to me and say, "we'd all like some food", and continue eating. While both "I'd like some food" and "we'd all like some food" are both true, I still don't have any food, and the second statement ignores that, doing nothing to rectify the fact that I have no food.
Yes, all lives matter, but when I see #BlackLivesMatter, I read "black lives don't seem to matter", not "black lives are the ONLY lives that matter". Saying "all lives matter" doesn't solve the fact that the folks saying "black lives matter" feel that in our society, their lives don't seem to matter as much as everyone else's.
Instead of making their pain all about you, by correcting #BlackLivesMatter to #AllLivesMatter, how 'bout acknowledging their statement? Black lives DO matter, and it's not right that anyone feels as if they don't. What can we do to move everyone towards the feeling that all lives matter equally? Because right now, all lives may matter, but some of them appear to matter a little less than others.