By that logic, clearly we shouldn’t care about soldiers lives, nurses lives, firefighters, etc.
They all chose to be that so clearly doing so signs away their worth.
Your logic is increasing flawed.
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Blue lives don't exist when their only existance is to diminish the struggle of black people. You didn't see a single person saying "Blue lives matter" until black people started fighting back against the system. Blue lives don't exist in the same way that black lives do. Not all lives matter until black lives matter.