Both of these chapters relate to the learning experiences of Jem and Scout in To Kill a Mockingbird. After complaining throughout the chapter that Atticus is old and feeble, they discover a new skill that their father has hidden from them: He is a crack marksman with a rifle. Atticus is not proud of this facet of his past, however. He indirectly relates the differences of true courageousness following Mrs. Dubose's death when he remarks that
"I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand."
Mrs. Dubose is the one with true courage, Atticus says.
"It's when you know you're licked before you begin but you begin anyway and you see it through no matter what."
Atticus will later display this same kind of courage when he tackles the Tom Robinson case, knowing beforehand that he cannot win.
In my opinion, you could write something about the cycle of life. There is a time and place for everyone and thing in the order of our world. Each situation is slotted into a master scheme of time. But all things have since our study of this world eventually come to an end. Both the "mad dog" and Mrs. Dubose had their time, and their times have come to an end. It is time for other things and for some reason, these two items are being removed from time.
I would say that one of Harper Lee's messages is that racism needs to be over. She was writing in the late 50s and was writing about the 30s. The Civil Rights movement was just about here, in fact her work may have contributed to the movement. Racism had a time in our history, we learned from it, but now it needed to be done.
Both the mad dog and Mrs. Dubose were put down with dignity. Atticus shot the dog because he was the only one who could kill the dog in one shot, minimizing the dog's pain. Mrs. Dubose needed the children's reading to help her not think about her pain as she worked to die free. In a way, Atticus is trying to put racism down, in its place in history with dignity. He is not helping the black man kill or defeat the white man cruelly, but he is working within the court system to get it done right.
Both events in the novel reveal aspects of the characters involved which give them an extra facet of humanity. When Atticus shoots the dog, he is revealing to his children an aspect of his character which they have never seen before. Both Scout and Jem see their father as 'old' and stuffy: they have never encountered the 'one-shot Finch' known to the other townspeople. After this event the children can see their father as heroic - something the adult reader sees also in his actions defending Tom Robinson.
Mrs Dubose is seen as a bigoted and cruel woman by the children. Scout refers to her as:
the meanest old woman who ever lived.
By being made to read to Mrs Dubose after destroying her flowers, Jem learns humility from his father whom she was insulting and finds out the meaning of courage when he finds out he was assisting in her beating her morphine addiction. The children learn that we do not always understand the motivations of other people and this viewpoint assists the reader in recognising the injustices of the Robinson trial.