Scout never actually fought with Cecil Jacobs. She came close, but her promise to Atticus reminded her that if she did fight him,
... I would let Atticus down. Atticus so rarely asked Jem and me to do anything for him...
The primary reason that Scout was about to square off with Cecil was because he had told her in front of her schoolmates in the school yard that Atticus "defended niggers." Scout didn't exactly know what it meant, but it wasn't enough for her to break her promise to Atticus about fighting anymore. Even after Scout demanded that he "take back" his accusation, which Scout knew was an insult--as if Atticus had been "runnin' a still"--she refused to fight. Cecil's final attempt to get her to break her promise, by taunting "Scout's a cow--ward!", also failed to work.
It was the first time I ever walked away from a fight.