Scout certainly starts off on the wrong foot her first day of school. First, she demonstrates that she knows how to read. Second, she demonstrates that she knows how to write. Third, she tries to offer an explanation for Walter Cunningham's behavior when Miss Caroline tries to give him money for lunch.
It may seem odd that a teacher would be angry over a child who could already read and write, but as we read this section of the book, we can see what an insecure and rigid teacher Miss Caroline is. She says that Atticus and Calipurnia have damaged Scout by teaching her how to read and write, so we can see that she believes there is only one way to learn, her way.
Her lack of understanding about the Cunninghams stems from the fact that she is not a local woman and has no knowledge of any local families. When Scout tries to explain, Miss Caroline is made even more insecure.
A good teacher is always happy to learn about new ideas and about his or her students, and the "portrait" of Miss Caroline is one of a teacher who is not very successful.
Scout has high hopes for her first day of school. She had longed stared out in the distance to catch a glimpse of Jem playing in the schoolyard with the other children. She wanted to be a part of this experience called school.
On the first day of school, Scout joins her class. Miss Caroline is her teacher. Scout unknowingly annoys Miss Caroline and makes her mad. Scout makes three mistakes:
1. Scout knows how to read, and she reads well. Miss Caroline had expected a class full of hungry, unlearned young minds. She asks Scout to identify the alphabet on the blackboard:
... as [Scout] read the alphabet a faint line appeared between [Miss Caroline's] eyebrows, and after making [her] read most of My First Reader and the stock-market quotations from The Mobile Register aloud, she discovered that [she] was literate and looked at [her] with more than faint distaste (To Kill a Mockingbird, Chapter 2).
Miss Caroline tells Scout to stop reading at home with her father. She wants to "take over from here and try to undo the damage." Miss Caroline wants to teach Scout how to read in her own way, which is by the methods she learned in college. She is annoyed that someone else had taught Scout to read in the "wrong" way.
2. Scout starts writing a letter to Dill in cursive. Miss Caroline notices and stops her. She tells Scout that her father needs to stop teaching her to write, as well. She also informs Scout that for now she should learn to print, because she will not start writing in cursive until the third grade. She is upset again that Scout had been taught to write in a way that she viewed as incorrect.
3. Walter Cunningham, Jr. does not have lunch and Miss Caroline tries to loan him a quarter. He refuses, but she insists. Scout speaks up, trying to explain to Miss Caroline that people in the Cunningham clan do not borrow money from anyone. Miss Caroline thinks that Scout is being impertinent, and she punishes her with smacks on the hand with a ruler.