Obviously the fact the Black people have killed Black people before has nothing at all to do with the murder of Mike Brown. As Jon Stewart so aptly notes, to bring it up means to not only ignore the fact that plenty of Black people do care about, and are doing plenty to combat. Black-on-Black crime (just because you don't bother to look for something doesn't mean it doesn't exist), it also means you can't see the difference between someone being murdered by a gang member and someone being murdered by a uniformed law enforcement officer who has sworn to protect the citizens of their town. Now, gangs and police forces actually share quite a few similarities in both organization and culture, but I think it's pretty uncontroversial to suggest that police should probably be held to a bit higher standard than gang members.
But arguing all the specific points of why shouting "Black-on-Black crime also exists!" every time a white supremacist murders a Black child is pointless; I have a hard time believing the people making that argument actually think it's a realistic rebuttal to such stark evidence of institutional racism. Instead it's just a classic derailing tactic designed to push the conversation to all those horrible things Black people have done, conveniently leaving behind the murder of an innocent Black child by someone who has yet to be arrested or even investigated for their blatant crime.
Ultimately bringing up Black-on-Black Crime™ simply reveals how profoundly racist the person mentioning it is. Not just for the reason explicated above (and much more eloquently by thousands of of other outlets), but because it's essential premise is "There's another dead Black kid. Who gives a shit who killed them? They're all violent criminals who are going to die young anyway." Because the only reason completely unrelated murders become relevant to the case of Mike Brown (or Eric Gardner, or Amadou Diallo, or Sean Bell, or Trayvon Martin, or the hundreds of others) is if you think Black lives have no value, so the specific cause of their death is a pointless concern.
If you doubt me, spend a few minutes researching the media's response to literally any non-Black murder victim. Simply put, you will never find an article wondering why white people don't spend more time worrying about white-on-white violence, why gay people don't spend more time worrying about gay-on-gay violence, while women don't spend more time worrying about women-on-women violence, etc. (Obviously Black people can be gay and/or women as well, but in the question of whether a murder victim deserves any sympathy, Blackness seems to trump all else).
Why don't we ever find these things? Well, it could potentially be many reasons. But if the aftermath of Mike Brown's murder (and so many others like it) has taught us anything, it's that these non-Black lives have value to us. It's that we as a nation assume Black people had it coming, whether for something they did at that moment or something they did years earlier. And the only reason to feel that way would be because you feel Black lives have no value. After all, there may be a reason why this has become one of the central rallying slogans in the wake of Brown's murder: