Scout’s outburst is a result of Cecil Jackson saying her father “defended niggers.”
Scout has a temper. This is why her father told her he would “wear her out” if he caught her fighting. He knows it is unladylike and thinks she is too big for fighting. He also realizes that Scout is going to hear much worse as the trial looms closer.
Atticus never actually hits his children, despite all of his threats to do so. Instead of punishing Scout, Atticus has a meaningful heart to heart conversation with her when she asks him if what Cecil said was true. Atticus objects to her using the word Cecil used, calling it “common.”
"I'm simply defending a Negro- his name's Tom Robinson… Scout, you aren't old enough to understand some things yet, but there's been some high talk around town to the effect that I shouldn't do much about defending this man.” (Ch. 9)
Scout may be young, but she is about to be thrown into the situation whether she is ready or not. This is why she describes the fight as “the beginning of a rather thin time for Jem and me” (Ch. 9). Children, and even some adults, have no qualms about targeting the Finch children because their father is defending Tom. Their racism prevents them from accepting the fact, and they take it out on his kids.