Burris Ewell's confrontation with Miss Caroline on the first day of school is dramatic and very revealing of his character. When Miss Caroline finds lice in the boy's hair, she tells him he must go home and treat them with lye soap and kerosene before returning to school. She also instructs him to take a bath before coming back. Burris laughs at her. She isn't sending him home, he says, because he was getting ready to leave anyway.
After hearing her class explain the circumstances of Burris's life at home, Miss Caroline asks the boy to sit back down. He defies her: "You try and make me, missus." Miss Caroline then tells Burris again to go home, threatening to call the principal if he refuses. "I'll have to report this anyway," she says. Burris responds with hateful, vulgar disdain:
The boy snorted and slouched leisurely to the door.
Safely out of range, he turned and shouted: "Report and be damned to ye! Ain't no snot-nosed slut of a schoolteacher ever born c'n make me do nothin'! You ain't makin' me go nowhere, missus. You just remember that, you ain't makin' me go nowhere!"
He waited until he was sure she was crying, then he shuffled out of the building.
Burris Ewell is indeed "a mean one, a hard-down mean one," as Little Chuck Little says to Miss Caroline.
In Chapter 3, Miss Caroline gets spooked after seeing a "cootie" crawl out of Burris Ewell's hair. After Little Chuck Little helps Miss Caroline settle down, she addresses Burris and tells him to go home and wash his hair. Burris immediately gets an attitude and tells Miss Caroline that he will not be returning to school for the rest of the year. After she tells Burris to sit down, he says, "You try to make me, missus" (Lee 19). Fortunately, Little Chuck Little intervenes again by threatening Burris. When Miss Caroline says that she will call the principal, Burris snorts and begins calling her derogatory names. Burris calls Miss Caroline a "snot-nosed slut of a schoolteacher" before he shuffles out of the building. Burris's rude attitude reveals his despicable character, and his words hurt Miss Caroline. After Burris Ewell leaves, the children comfort Miss Caroline at her desk.
Short answer: he calls her a snot-nosed slut.