All Americans suffer from killings at the hands of police when unarmed. Unarmed people killed by police are mostly non-black: (https://www.washingtonpost.com/graphics/national/police-shootings/ for 2015 and https://www.washingtonpost.com/graphics/national/police-shootings-2016/).
Clearly there is some non-race related driver for police killing unarmed people in the US. I'll speculate that it's related to the astronomic murder rate and violent crime rate in the US coupled with a very high rate of gun ownership. Policing in that environment is hard, involves shooting people, and inevitably must involve mistakes.
Black people ARE overrepresented among unarmed people killed by police relative to their population. Some people argue this is because black people are overrepresented among convicted criminals, but I think it's probably because of the sort of subtle racism against black people that is pervasive in the world.
However, this racism is not why the police are killing unarmed black people. Police are killing black people for the same reason they are killing unarmed white people: they think they are under threat.
The title "Black Lives Matter" in this context implies that police are especially killing black people without consideration for the value of their lives due to their race. This is a serious charge and would be infuriating if true. It could lead to a majority of black people (and many others) in the United States thinking that some police are either actively seeking to hunt and kill black people, or at best indifferent to killing black people. This belief would undermine the trust people put in the police to keep them safe from criminals etc. That is dangerous. Furthermore, it could lead people to actively pursue a war on police in the pursuit of self defense, which is also dangerous.
It is divisive because all Americans suffer from violence and police violence in particular. All Americans would benefit from a solution to this problem. By framing it as a black-only problem, when it is not in fact a black-only problem, it alienates the majority of the country that has a stake in solving the problem. Moreover, by pitting themselves against the police as an evil group that condones 21st-century racist "lynching", BLM alienates all those people whole value the protective role of police in society. All of this serves to dilute or undermine the legitimate BLM causes of 1) addressing real racism and 2) reducing violence in society and among police.
EDIT: I still think most individual police killings of unarmed people is mostly due to policing errors and not mostly due to racism. I also still think the overrepresention of black people in this group is largely an example of institutional racism plus unconscious bias in threat perception, and of course this should be addressed. A lot of people say BLM's message stops here, which I am not buying.
I still think BLM as a movement is further implying that unarmed black people are being killed for no reason other than their race, or that race is far and away the main factor. There's been much discussion of the semantics of institutional racism plus implicit bias vs. overt racism, and what it means for race to be the primary factor in a killing, none of which is very compelling to me. I think we can agree to disagree here.
Where my view is changed is primarily that BLM's (inaccurate) portrayal of cold-blooded police killings is a powerful rallying cry with ultimate political implications (more equality of opportunity, less racism, less police brutality) that I support, and whose benefit outweighs the costs of divisiveness and amplified antagonism towards police. https://www.reddit.com/r/changemyview/comments/4s07vj/cmv_black_lives_matters_message_that_police_are/d55jcto
I also awarded a tentative delta on the idea that there may well be a second variety of implicit bias beyond the threat skew, whereby police value black people less and will therefore have a lower threat threshold for shooting and killing. This is plausible and strikes me as reprehensible in a way that approaches overt racism to a far greater degree than the threat bias. However, evidence was shown that the threshold for shooting black people is actually higher, not lower: https://www.reddit.com/r/changemyview/comments/4s07vj/cmv_black_lives_matters_message_that_police_are/d55l5md