If when someone says "Black Lives Matter" you quickly respond with "All Lives Matter" then I have a few things I want to say to you.
At least pause for a moment before replying and ask yourself why this person is saying Black Lives Matter. Of course they know and agree that all lives matter. But that isn't what they're saying. They're saying that Black Lives Matter not because they're more important than white lives or cop lives, which seems to be how you're interpreting it, but because a lot of black people are being killed and the justice system does not seem to care.
I think we all know that if Trayvon Martin, for example, had been a white teen, and George Zimmerman had been a black adult man, the outcome would have been different. But because he was black, and black lives don't matter, Martin is dead and Zimmerman is free.
There have been a seemingly endless series of graphic stories, many of them on video, of white police killing black people, and getting off. I suspect this has been going on all along, but now with the wide use of smartphones, we're actually seeing it, visually, as we couldn't have seen it before. Now it's not their word against a cop's. The video provides testimony that is impossible to refute.
If you were black, and you saw this happening, you might be inspired to do more than say something like Black Lives Matter. Your rage and fear might overwhelm you. So the first thing I would say to a black person who said Black Lives Matter is thank you for containing the rage you must feel, that I would feel if I were in your shoes, that I feel in a small way on your behalf, at the cruelty and callousness of our system and culture. Then I'd ask if there was anything I could do to help.