Logical fallacy's galore. To think the people involved in "black lives matter" don't value all lives is a mis-characterization. It was a slogan to bring attention to an issue that has disproportionately affected "african american" people. A slogan like "have a coke and a smile" is also not saying that you cannot smile without a coke. If there were a rash of any underrepresented group being mistreated or killed while under police custody anyone and everyone should be outraged.
To believe in the ideal that no one should be marginalized is not the same as being a proponent of the opposite. That's one of the problems with discourse in dealing with issues like this because things are painted as mutually exclusive when there is a lot of overlap and a range of viewpoints.
Women, who make up the majority of people in the USA are also the most likely victims of domestic violence. No one would be thinking it sexist to push for and end to domestic abuse with a slogan that mentioned "Women". And though men are also victims of domestic abuse it is not to the same degree.
Violence is terrible when it happens to anyone, be they law enforcement or civilians or health care workers. When I realized how things are framed shapes perception and started to look at the statements and comments being made it helped me to realize that this type of thought process is deep in the Jehovah Witness pysche.
Either you are for us or against us. Either you love this or you hate it. That's not true. Change a statement into something equivalent and it's easily seen. Either someone loves Jesus or they hate Jesus. What about people who like him somewhat and dislike him somewhat? If someone derived your views on ice-cream based on something like "Do you want to eat ice cream now" and inferred that if you answered "no" that you never wanted to eat ice cream or if you answered "yes" that you always wanted to eat ice cream would miss the possibility that many people only like ice cream some of the time. (I was going to specify a flavor but that might have detracted from the point.)
I prefer to call this type of statement false dichotomy instead of a "black and white fallacy" which it is also known as.