Scout Finch is immature because:
1. SHE IS EASILY PERSUADED TO FIGHT. We see this in the beginning as she wants to fight Walter Cunningham, and later she fights with her cousin Francis for calling her father a "nigger-lover".
2. SHE DOESN'T UNDERSTAND THE INNUENDO OF ADULTS. When adults talk about something, she doesn't catch their meanings or jokes. Atticus gives Scout a direct dictionary definition of rape because he's thinking that she isn't going to ask anymore questions with a phrase like "carnal knowledge". Furthermore, when Scout is in the middle of all the men who are ready to fight Atticus out in front of the jail, she doesn't even seem to know what's going on, she just remains friendly as ever.
3. SHE DOESN'T UNDERSTAND WHY RACE IS AN ISSUE. She just accepts that it is in her father's cases. However, when it comes to Mrs. Gates talking about persecuting the Jews, she does recognize that what the whites do to the blacks feels an awful lot like that. She still struggles with why that happens though.
Being a coming of age novel, the book demonstrates great growth in Scout during the whole book so she has to be immature at some points for the book to reveal these learning moments.
Scout displays her immaturity through her reactions when she doesn't get her way or is upset with someone. At the beginning of the novel, Calpurnia chastises Scout for her manners during dinner. Scout gets upset that Calpurnia yelled at her and says that she is going to drown herself in Barker's Eddy to make Cal feel bad. Also, Scout's first reaction is to fight others when she is provoked.
Scout portrays her immaturity by believing in the false rumors that surround her reclusive neighbor, Boo Radley. Despite the fact that she is never threatened by Boo, Scout continues to believe that her neighbor is a "malevolent phantom."
Scout also displays her immaturity through her inability to comprehend certain situations. In Chapter 15, Scout runs out into the middle of a mob just to listen to what her father is saying to the men. She is completely unaware of the dangerous situation that she has entered.