slavery. She says to Cassie:

"The people who needed slaves to work in their fields and the people who were making money bringing slaves from Africa preached that black people weren't really people like white people were, so slavery was all right" (page numbers vary by edition).

Mama explains that even though slavery has ended, people like Mr. Simms still cling to the false idea that African-Americans are inferior to white people. 

Mama explains that Big Ma was protecting Cassie when she made her apologize.

Cassie is like most young girls.  She is trying to figure out how the world works.  As far as she is concerned, Lillian Jean Simms is just a bratty girl and has no right to tell her what to do.  Lillian Jean  sees it differently.  She considers herself superior because she is white and Cassie is black.  Unfortunately, Lillian Jean has learned to feel this way from her society.  Cassie gets a hard lesson in race and inequality.

The incident occurs because Lillian Jean wants Cassie to get off the sidewalk.  Her brother Jeremy, who is a sort of friend of Stacey’s, tries to tell Lillian Jean that Cassie isn’t doing anything but Lillian Jean responds that Cassie is standing in front of her.  Her father pushes Cassie off the sidewalk, and demands an apology when Big Ma says they are going home. 

“Not ’fore she ’pologizes to my gal, y’all ain’t,” said Mr. Simms.
Big Ma gazed down at me, fear in her eyes, then back at the growing crowd. “She jus’ a child—”
“Tell her, Aunty—”
Big Ma looked at me again, her voice cracking as she spoke. “Go on, child . . . apologize.” (Ch. 5) 

Big Ma knows that there might be trouble if the Simmses do not get what they want.  This is why she is afraid.  She can’t stand up for Cassie then, and she can’t explain things to her.  She just has to get her to apologize so they can get out of there.  It is a terrible thing to see your granddaughter go through, but she has no choice.

Stacey tells Cassie not to blame Big Ma.  He is older, and understands the way the world works better than Cassie does.  Later, at dinner, Cassie complains that Mr. Barnett waited on the whites before the blacks in the store, and when she let him know he banned her.

Mama explains to Cassie that Big Ma was trying to protect her when she forced her to apologize to Lillian Jean.  Mr. Simms acted the way he did because as a white man, he felt superior.

“Because he’s one of those people who has to believe that white people are better than black people to make himself feel big.” (Ch. 6)

Cassie asks why he doesn’t know better.  Mama tells her this is just the way things work.  Although things have changed since the days of slavery, Mama tells her that people like the Simms hold onto the belief that they are superior because “they have little else to hold on to.”  Things are better, but still not equal.

Big Ma, Cassie Logan's live-in grandmother, to her astonishment permits her to ride in the wagon to the nearby Mississippi town of Strawberry on market day. Later that day, preoccupied with the shame of a racist encounter with the manager of the town's general store, Cassie accidentally bumps into Lillian Jean Simms, a white girl her own age. Not content with a simple apology, the Simms girl demands Cassie get down from the sidewalk into the road. As Cassie refuses this further humiliation, Mr. Simms intervenes and forces her into the road. Into this ugly confrontation steps Big Ma who insists that Cassie apologize. She does so, reluctantly, but is infuriated with her grandmother. Later, as Cassie prepares to go to bed, Mama explains Big Ma's actions:

"Big Ma didn't want you to be hurt...That was the only thing on her mind...making sure Mr. Simms didn't hurt you."

Not satisfied with that answer, Cassie questions the endemic racism of her environment:

"How come I gotta go 'round calling her 'Miz' like she grown or something?"

Mama, troubled because her only daughter has had her first encounter with brutal inhumanity, explains that Mr. Simms pushed her into the street "because he's one of those people who has to believe that white people are better than black people to make himself feel big."

As Cassie stares at her uncomprehendingly, Mama retells the story of slavery and Christianity corrupted and emancipation:

"Even though seventy years have passed since slavery, most white people still think of us as they did then - that we're not as good as they are - and people like Mr. Simms hold on to that belief harder than some other folks because they have little else to hold on to."

Still not placated by this unjust state of affairs, Mama reminds Cassie that however unchosen the colour of one's skin is, she has infinite "choice over what we make of our lives once we're here...And I pray God you'll make the best of yours."