Mrs. Dubose and the Finch children do not mix. Up until this point, Jem and Scout would wait in front of Miss Rachel's house for Atticus to come home in the evenings; but Jem decides that's cowardly, and they must go past the evil, old woman's house to the corner from then on. As a result, they get an ear-full every time they do. She's rude, has no filter, drools, and has a gun under her seat. For a little girl, that's pretty scary. When Atticus speaks to Mrs. Dubose, he is a perfect gentleman, but Scout is probably sitting there watching to see if the old woman will pull out that gun and shoot her father! Scout is really impressed by Atticus' behavior and explains it like this:
"Atticus would sweep off his hat, wave gallantly to her and say, 'Good evening, Mrs. Dubose! You look like a picture this evening'. . . He would return his hat to his head, swing me to his shoulders in her very presence, and we would go home in the twilight. It was times like these when I thought my father, who hated guns and had never been to any wars, was the bravest man who ever lived" (100).
In a way, it's as if Scout's father is the gallant knight confronting the mean dragon and saving the princess from her fiery breath. Atticus saves the day.
Scout thinks that Atticus is the bravest man in the word when he talks to Mrs. Dubose. Scout considers her a horrible woman, and she cannot imagine how Atticus can make small talk with her and tell her she is a “picture” (though he never says of what).
He would tell her the courthouse news, and would say he hoped with all his heart she'd have a good day tomorrow. He would return his hat to his head, swing me to his shoulders in her very presence, and we would go home in the twilight. (ch 11)
This statement seems to contradict Scout’s fear that Atticus is not interesting. She appreciates his ability to interact with the mean old woman, and even be nice to her. Scout cannot imagine why he would want to, and thinks it is brave of him to even try.