Mama teaches Cassie that respect given because it is demanded is not respect at all.
Cassie is upset because after Lillian Jean Simms pushed her off the sidewalk, Big Ma made Cassie apologize to her instead of the other way around. Mama explains to her that in "the way of things" in the South at that time, most whites consider themselves to be better than blacks, and demand that blacks act in deference to them. When Cassie protests the unfairness of this situation, Mama explains that people who think like this, like Lillian Jean's father, do so because they want to make themselves "feel big". The inadequacy is within them, not the black people who are their victims.
"White people may demand our respect, but what we give them is not respect but fear. What we give to our own people is far more important because it's given freely. Now you may have to call Lillian Jean 'Miss' because the white people say so, but you'll also call our own young ladies at church 'Miss' because you really do respect them" (Chapter 6).
Mama's message is that respect freely given is the only important kind.