Yes. Just like when you are with your family at the diner, the phrase, "We should all get to eat what we ordered" is the truth. However, if it's coming from your spouse after the kitchen gave you the wrong order (while everyone else got the right order) and you said, "I should get to eat what I ordered", it might come across as dismissive and mean. "What, does she think I don't think they should get what they ordered? They already got what they ordered; everyone else is doing just fine!" Fundamentally, this is the problem here:
It doesn't. It just doesn't. In a vacuum, with absolutely no cultural context, it's an equitable, reasonable statement. But we aren't in a vacuum, and given the context, it's what your hypothetical spouse said to you at your hypothetical restaurant: a dismissive response to a group of the populace saying, "Hang on, we're being treated unfairly", dismissing their claims as irrelevant and saying "we all should be treated fairly" as if their problems didn't matter.
The problem here is that everyone else already is being treated fairly, and nothing in #BlackLivesMatter devalues anyone else's life. What, do you think the people saying "Save the rainforest" mean "Save only the rainforest and slash and burn all the others"? No, they're drawing specific attention to a specific issue. Same deal with #BlackLivesMatter. Of course the people saying that understand that white lives matter too. EVERYONE UNDERSTANDS THAT WHITE LIVES MATTER. Even the police. At the same time, it seems like people don't understand that black lives matter. Not in the same way, anyways.