Black Lives Matter doesn't mean non-Black lives DON'T matter, what it means is that Black lives matter TOO. It's not saying Black lives are the only lives that count, that's not at all what BLM as a movement and philosophy is about. It's intended to draw attention to the inequalities Black people continue to face, both in the form of police brutality and on a wider societal scale.
Let me explain an allegory to the BLM vs. ALM debate. Imagine a street where one of the houses is on fire. The resident of said house calls the fire department. They arrive and put out the fire, focusing their hoses on the burning house. But, in the midst of all of this, a resident from the house next door, which is not on fire, requests that the firefighters spray down his house as well. Furthermore, he demands that all the houses on the street be sprayed down.
BLM is like the firefighters putting out the fire in the burning house. If any of the other homes were to catch fire, they would put those fires out, but the rest of the homes are safe, so they need to take care of the burning one. ALM is like demanding that all the houses get sprayed, despite them not being on fire.
ALM has a good intention behind it, I will concede that. But again, if you respond to BLM with ALM then you don't understand the point of BLM. BLM does believe that all lives matter. They believe White lives matter, they believe Asian lives matter, and of course they believe that Hispanic lives matter. But Black lives are all to often treated as expendable and unimportant, and BLM aims to change that.