Scout's antagonistic cousin, Francis Hancock, "the most boring child I ever met," made the mistake of repeatedly taunting her with the epithet "nigger-lover"--referring to Atticus. Scout wasn't quite sure what it meant, but she could tell from Francis' tone that it wasn't good. But Francis kept it up, running into the kitchen each time, where he was protected by Aunt Alexandra. So Scout waited patiently, pretending to take a passive stance, until Francis made the mistake of going out into the yard, beyond the scope of Alexandra's protection. When he thought Scout "sufficiently subdued," he once again
...crooned softly, "Nigger-lover..."
This time I split my knuckle to the bone on his front teeth.
Scout received a spanking from her Uncle Jack for her pugilistic display, but after Scout explained her reasons to him, Uncle Jack was ready to deal out some punishment to Francis himself.
In Chapter 9, the Finch family gets together for Christmas dinner, and Scout ends up fighting her cousin after he makes several derogatory remarks about Atticus. After dinner is over, Scout and Francis head outside, where he begins to make rude comments about her father. Francis tells Scout,
"Grandma says it's bad enough he lets you all run wild, but now he's turned out a nigger-lover we'll never be able to walk the streets of Maycomb again. He's ruinin' the family, that's what he's doin'" (Lee 52).
Scout gets extremely upset at Francis's comments and attempts to hurt him, but Francis manages to run away. Although Scout is not fully aware of the meaning of "nigger-lover," she understands that it is a negative term. When Francis is at a safe distance, he continues to yell "nigger-lover!" (Lee 52) Scout responds by pretending that she is not bothered anymore by Francis's comments. Francis feels confident enough to approach Scout and continues making fun of her father. As Francis begins to call Atticus a "nigger-lover" again, Scout punches him in the teeth, splitting her knuckle to the bone. Uncle Jack ends up stopping the fight, and Atticus's family heads home.
This question has already been asked and answered right here on eNotes. Here is a link for you: http://www.enotes.com/to-kill-a-mockingbird/q-and-a/why-does-cousin-francis-tell-scout-about-dills-120681
They do not get along and what happened was Francis got on her bad side and insulted Dill but also insulted her father to where she could not take it. Her father always told her to hold in her anger and stop fighting so she waited until he was an arms length away to start fighting with him.