To illustrate, a black person once asked me, "you don't like black people do you?," to which I for humorous purposes responded, "no." An elderly colored lady immediately said to the guy, "don't listen to him honey; he don't like white people either."
See, the statement, "I don't like black people," is not necessarily racist, and my example illustrates that the IMPLICATION is absent, but despite that, it's highly SUGGESTIVE that it is.
The statement, "black lives matter" doesn't IMPLY that the only lives that matter are black lives, but (and especially when spouted by blacks towards whites in an angry tone) the phrase highly SUGGESTS which lives they think matters.
The idea of retorting that all lives matter is understandable, but it minimizes the reasoning behind why the phrase ever come to be. If blacks are disproportionately taken at the hands of police, the phrasing by blacks is a reminder that not only do the lives of non-blacks matter, but their lives matter too.
So, the phrasing is unfortunate because of the negative suggestion that either only their lives matter or their lives are more important, and the phrasing all lives matter minimizes the point of saying it to begin with, but more appropriately, "black lives matter too" reinforces some rather acceptable ideas like the lives of blacks should matter to those in power who are too quick to act like their lives don't.