John: Hey, my house is on fire...let's put it out!
Mary: No, let's spray water on all the houses, because all houses matter!
This would be a valid response, if one were only responding to the organization's name. However, in fact, a lot of people who say "All Lives Matter" are responding to Black Lives Matter the movement.
When BLM excludes non-blacks from their meetings, demands whites to move to the back, encourages attacks on police officers, and violently attacks whites or anyone who disagrees with them — it doesn't seem egalitarianism is at the heart of your movement.
When the head of BLM Toronto talks about killing men and white people, some people are going to have major reservations about your movement. And, I realize that this was tongue-in-cheek, however, we all know if the same were said about 'women and black folks' by a MAGA hat wearing Trump supporter, BLM would lose their minds.
When BLM zealots murder police officers and your response is 'I don't support it, but I understand why they did it', here again, it doesn't appear that you believe all lives matter.
Someone who believes all lives matter wouldn't be violent against the innocent and respond to perceived racism with more racism.
Furthermore, many people don't like the notion that they must prove a negative. The name suggests that our society doesn't believe that black lives matter, so, apparently, the onus is on us to prove the opposite. Yet, black lives are all we talk about and sympathize over, even when the victim was engaging in at-risk behavior that lead to his death.
If you can't see the hypocrisy in your movement and how 'all lives matter' is not at the core of your movement, then, to quote the above meme, "you are part of the problem."