At the beginning of Scout's second grade year, she and Jem were more inclined to venture towards the center of town and leave their neck of the woods for a time. Rather than cross the street like a coward to avoid walking past Mrs. Dubose, Jem bravely walked along that side of street. As a result, he and Scout would have to listen to her yell at them even though they were always polite to her. She would get upset to hear Jem call his father "Atticus"; she got upset because Scout wore overalls; she even spoke about the children's deceased mother and how they would have been raised better had she lived. The children did everything in their power not to talk back to her. Scout explains how Atticus taught Jem to handle the situation as follows:
"Countless evenings Atticus would find Jem furious at something Mrs. Dubose had said when we went by.
'Easy does it, son,' Atticus would say. 'She's an old lady and she's ill. You just hold your head high and be a gentleman. Whatever she says to you, it's your job not to let her make you mad'" (100).
That's easier said than done when the old lady won't keep her mouth shut. Eventually, Jem goes berserk with the help of Scout's toy baton and cuts off the tops of all Mrs. Dubose's camellia bushes. To make up for losing his head and not acting like a gentleman, he has to read to Mrs. Dubose for a month.
In Chapter 11 of To Kill a Mockingbird, Mrs. Dubose, a neighbor, constantly taunts Jem and Scout. She calls Scout ugly and criticizes Atticus for not having remarried after his wife died. Jem and Scout develop an intense dislike towards her, but Atticus tells Jem, “She’s an old lady and she’s ill. You just hold your head high and be a gentleman. Whatever she says to you, it’s your job not to let her make you mad" (page numbers vary by edition). Atticus asks Jem to turn the proverbial cheek to Mrs. Dubose.
Later, Jem and Scout discover that while Mrs. Dubose is not very pleasant, Atticus has sympathy for her because she is addicted to morphine and decides to kick her addiction before she dies. This process is very painful for her, and it shows her considerable strength of character. Atticus teaches his children to have sympathy for people who seem unsympathetic because, as he reminds them, they don't always understand other people's lives. Mrs. Dubose is a character in the novel who seems undeserving of kindness but whose deeper pain compels sympathy.
At the beginning of this chapter, before Mrs. Dubose really makes Jem angry, Atticus has given Jem advice about how to react to her. He tells Jem, basically, that he must ignore Mrs. Dubose. He tells Jem that he has to hold his head up, be a gentleman, and not let her make him angry.
Of course, later in the chapter, Jem is unable to follow this advice. Presumably he gets angry because she says Atticus is no better than the black people or "trash" that he works for. At this point, Jem cannot follow the advice (which he has repeated to Scout) and gets very angry.