The answer to this question can be found if we examine the story that Mike tells Bryon earlier on in the chapter. He says how he was in a drugstore one night with a gang when a black woman entered and the gang began to bother her. This, for some reason, really annoyed Mike, so he stepped in and told the gang to stop it:
When one of the guys grabbed hold of her and really got crude, I got fed up. I went over and said, "Let her go," like I meant it.
Mike therefore steps in and stops his gang from bothering the black woman further. She leaves the drugstore and Mike offers to give her a lift home. It is only when she reaches her home that she begins crying and then she tells her various friends at her home that Mike had bothered her and she wanted him killled.
We can infer that the reason for this behaviour is that, having felt so powerless herself among whites just an hour ago, the black woman has a chance to reverse the situation and get her revenge, making a white feel like she did. Her command is therefore based on the desire to let Mike, even though he technically saved her, experience what she experienced. It has nothing to do with Mike but rather the racism and discrimination that the woman has experienced and her desire to turn the tables.