1. Because I care about the rights of non white people in a historically racist country
2. You did not, but the point of saying 'black lives matter' is saying that all lives matter, but the black community is being discriminated against by a small part of the white community (Not all, just a few), and the reason we only say 'black lives matter' is because white privilege exists and black people are not given the same privileges that white people are.
3. To a very very small group, it always means the worst that could possibly be implied, but I am extremely confident that the vast majority of people in BLM do not think of it that way