She believes that executing people is not going to better our society. Even though two of her family members were assasinated she believes that who did it should not be executed. King also mentions in this passage that there is always that chance that someone innocent could be executed which is a chance that shouldn't be taken. The death penalty is designed to discourage people from comming crimes of violence. King's argument is that when people commit these types of crimes, they are not in the right frame of mind to think about what is going to happen to them, including the death penalty.
Legalized murder is a step in the wrong direction and is setting a bad example.
Maybe add a thesis statement and follow that order of ideas throughout the essay. The racism is the thing that should be done away with. It doesn't have much connection with the death penalty. The courts job is to give us, the citizens, justice.