In the thread from Reddit comes this explain it like I’m a 5 year old response: (Thank you GeekAesthete for your brilliant work)
Imagine that you’re sitting down to dinner with your family, and while everyone else gets a serving of the meal, you don’t get any. So you say “I should get my fair share.” And as a direct response to this, your dad corrects you, saying, “everyone should get their fair share.” Now, that’s a wonderful sentiment — indeed, everyone should, and that was kinda your point in the first place: that you should be a part of everyone, and you should get your fair share also. However, dad’s smart-ass comment just dismissed you and didn’t solve the problem that you still haven’t gotten any!
The problem is that the statement “I should get my fair share” had an implicit “too” at the end: “I should get my fair share, too, just like everyone else.” But your dad’s response treated your statement as though you meant “only I should get my fair share”, which clearly was not your intention. As a result, his statement that “everyone should get their fair share,” while true, only served to ignore the problem you were trying to point out.
That’s the situation of the “black lives matter” movement. Culture, laws, the arts, religion, and everyone else repeatedly suggest that all lives should matter. Clearly, that message already abounds in our society.
Just like asking dad for your fair share, the phrase “black lives matter” also has an implicit “too” at the end: it’s saying that black lives should also matter. But responding to this by saying “all lives matter” is willfully going back to ignoring the problem. It’s a way of dismissing the statement by falsely suggesting that it means “only black lives matter,” when that is obviously not the case. And so saying “all lives matter” as a direct response to “black lives matter” is essentially saying that we should just go back to ignoring the problem.