Why responding to "black lives matter" with "all lives matter" is a statement of racism.

Responding with "all lives matter" misrepresents the position of the anti-racists, pretending that their slogan "black lives matter" means "only black lives matter". But they don't say, or mean, "only".

Properly understood, "black lives matter" is not racist at all. It is a compact way of saying that "black lives matter just as much". It is a rebuke to the covert, racist "black lives don't matter" movement, which few overtly endorse but many act to support.