On the one hand, you have the slogan, black lives matter. Most folks are down with that cause and sentiment, even us dirty, rotten, mean conservatives. It would be foolish and callous not to be, unless you are an out and out racist. The problem is, the slogan is very much tied to an organization that has questionable methods and leadership. Not to mention, is an indirect shill for the democrat party. And I use the term, indirect very loosely. They are certainly a fantastic fund raiser for team Dem.

I think that the retort of all lives matter is more a gut response to throw shade at BLM, the organization, not the sentiment. And it is pretty dumb but it's understandable, it's knee jerk. I find BLM to be a detestable organization and just another pawn in the lefty/righty politics game.
You can hate the player and still give the saying a nod. But BLM the org, makes it difficult to be compassionate.

The sentiment and the org conjure two very different feelings for me, personally. I'm sure I'm not alone. I have two politically active, very good friends at work who are black. The conservative one mocks BLM and belittles it. The other, who has always voted dem but is hoping for a viable third party after all the pandering, you can't say anything wrong about BLM in front of him. So those two dudes fight it out. It's pretty interesting.