Scout fights because she has a temper and she is very sensitive. She is too young to really understand why people do the things they do.
Scout has not learned how to see things from others’ points of view. This is why she gets into fights. Atticus has some important advice to share with Scout.
“[If] you can learn a simple trick, Scout, you'll get along a lot better with all kinds of folks. You never really understand a person until you consider things from his point of view … until you climb into his skin and walk around in it." (ch 3)
She has plenty to fight about. Since her father has been appointed to Tom Robinson’s case, Scout is finding herself needing to defend her honor on a regular basis. Scout knows she is not supposed to fight. Her father has tried to explain that it is not the best way to solve problems.
Atticus had promised me he would wear me out if he ever heard of me fighting any more; I was far too old and too big for such childish things, and the sooner I learned to hold in, the better off everybody would be. (ch 9)
In the end, Scout does learn the art of empathy. It is part of growing up. She begins to see that not everyone appreciates what her father is doing, but he is standing up for what he believes in. That is all that matters, and she can be proud of him for it.