Black Lives Matter

""...as a person with a lawyer brain, I have to say…"

This is an attempt at an Argument from False Authority Fallacy. Being a lawyer has no bearings on whether the claim will be accurate or not. If anything, lawyers are trained to defend a position, which is not much different than defending a bias really. 

"when you single out one race and say ‘that’ race matters. You ARE implicitly saying other races don’t matter as much."

This is a Non Sequitur  as the conclusion does not follow from the premise. To conclude that "Black Lives Matter" means that other races don't matter does not necessarily follow. 

Its also a Strawman Fallacy to say, "You ARE implicitly saying" and then go on to say something that they did not actually say.

when you single out one race and say ‘that’ race matters. You ARE implicitly saying other races don’t matter as much.

That is only one option. For example, if parents are witnessing their two children drowning and the wife turns to the husband and says, "Save Billy. Billy's life matters," the implication is clear. Another option is that the common perception of the race is that it doesn't matter, so stating that it matters is putting on equal ground with the other races. This is clearly what is meant with "Black lives matter."

I wonder why people don't get upset when people have "save the dolphins" signs and scream "save ALL animals!"

"...as a person with a lawyer brain, I have to say… when you single out one race and say ‘that’ race matters. You ARE implicitly saying other races don’t matter as much."

No, this is Illicit Contrast. When one says the phrase "Black Lives Matter", we can implicate that the speaker believes that the lives of black people are important. It is only black lives that are being spoken about here, and no relation to any other racial/ethnic group is made. Thus, the assertion that "one is claiming other races don't matter as much" is baseless, and can only be made if one is biased.

If we extend the claim to "Black Lives are the most important" (which isn't what BLM is about), then, we can safely infer the speaker is putting black lives on a pedestal. But that's only because we have the word "most", to function as a comparative. Without it, we can't suggest anything else.

There may be other evidence that a BLM supporter doesn't value other lives as much, but without observation, and this supplementary evidence, there's nothing else to infer - the statement alone offers no support to the comment from the article.

If one insists on 'All Lives Matter' in a conversation regarding disproportionate killings of black men by police, this is Missing the Point (ignoratio elenchi).

"You ARE implicitly saying other races don’t matter as much."

It's very simple really, what is implicit is that black lives ALSO matter .  This is only said because of the double standards that exist by which it is clear that those in positions of power don't think black lives matter. There is no implication whatsoever that other races (not really a thing) don't matter, and to say so shows either ignorance, stupidity, or dishonest cynicism 

"All Lives Matter" in response to Black Lives Matter is a Red Herring meant to derail discussion about the racism and persecution black people face by either broadening the topic to the point of uselessness or vilifying the movement for attempting to address those issues. It's also a racist dog whistle. Same with "Blue Lives Matter".

They're also Logic Chopping since they're nitpicking the name of the movement rather than actually addressing their points about the police violence, institutional racism, etc. It's like fretting over the Civil Rights movement having a broad name just because they were addressing specific civil rights pertaining to a specific demographic rather than all of them.