As much as "To Kill a Mockingbird" is about Scout, Jem's maturity plays a large role in the book as well. Scout gets concerned when she sees Jem involved in adult-like behavior--she thinks something is wrong with him. When Jem fights her back, Scout is pleased to know that Jem is still acting childish.
However, Scout tells the readers that Jem breaks the final code of childhood when he reports to Atticus that Dill has run away and admonishes Dill for worrying his parents. A year prior, Jem probably would have made a game out of Dill running away and not told Atticus. However, Jem's maturity requires him to speak up, and it angers Scout because she thinks Atticus will get mad and Dill will have to go home. She wants Jem to be on their side--not on the side of the adults.
To Kill A Mockingbird exposes the tragic consequences of racial prejudice and unchecked discrimination. In Maycomb County, the hypocritical churchgoers cannot see their own faults as they are too busy gossiping or criticizing others. Despite this, Atticus always tries to teach his children not to be judgmental and to never presume to understand the opinions of another person unless they have had an opportunity to "climb into his skin and walk around in it."
Now that the children are growing up, things are changing. Aunt Alexandra wants Atticus to send Calpurnia, who has helped Atticus raise his children in the absence of a mother, away, but fortunately Atticus will not hear of it. Scout has noticed though, how Jem is, "positively allergic to my presence," and she does not respond well when he gives her some friendly advice not to antagonize Aunt Alexandra. When Jem puts himself in the adult category, Scout can not bear his "superiority" and intends to do something about his threat to "spank" her. Atticus breaks up the "brawl" and they are both sent to bed, a fact which pleases Scout as she feels like they are a team again.
However, Scout's pleasure at being Jem's "equal" is short-lived. She finds what she thinks is a snake under her bed and elicits Jem's help. To their surprise, it is Dill, hiding after he has run away from home. After a far-fetched version of his escape and a more realistic version of his running away from home, Jem does not hesitate to call Atticus, something Scout feels breaks "the remaining code of our childhood," rendering Jem a "traitor." Fortunately, Atticus takes the matter in stride and Jem knows he has done the right thing so that Dill's mother will not worry about him but Scout, although she forgives him, is not happy that he would do something so adult.
There is slight tension between Jem and Scout throughout the book. This is especially pronounced at the beginning of the book. For example, Jem yells at Scout:
Jem looked at me furiously, could not decline, ran down the sidewalk, treaded water at the gate, then dashed in and retrieved the tire.
“See there?” Jem was scowling triumphantly. “Nothin‘ to it. I swear, Scout, sometimes you act so much like a girl it’s mortifyin’.”
Here is another example:
I was not so sure, but Jem told me I was being a girl, that girls always imagined things, that’s why other people hated them so, and if I started behaving like one I could just go off and find some to play with.
As the book progresses, Jem matures, as he is four years older than Scout. So, towards the end of the book, Jem hits his teenage years, while Scout remains a little girl. This means that he is leaving behind Scout in terms of understanding and education. This makes Scout feel alone. So, when Jem and Scout fight, this reminds Scout of how it was.