Why, in Atticus's view, was Mrs. Dubose "a great lady?"

Jem despises Mrs. Dubose.  She insults Atticus and she is rude to he and Scout.  Despite Mrs. Dubose's cantankerous personality, Atticus refuses to insult or belittle their elderly neighbor.  Instead, he compliments her.  He tells Jem that "she was a great lady:"

"Jem, everything's all right.  You know, she was a great lady" (To Kill a Mockingbird, Chapter 12).

Jem is shocked by his father's words.  He asks his father how he can say such a thing about such an angry, mean person.  Atticus responds with his usual empathy.  He tells Jem that Mrs. Dubose was strong despite having many difficulties.  He admits that he and Mrs. Dubose had disagreed about many things, but despite this he had admired her.  His admiration for her had been a strong one.  He tells Jem that Mrs. Dubose was a courageous woman.  She had never given up, despite her hardships.  Atticus also explains that he had wanted to teach his son about courage through Mrs. Dubose:

"I wanted you to see something about her—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.  It's when you know you're licked before you begin but you begin anyway and you see it through no matter what.  You rarely win, but sometimes you do.  Mrs. Dubose won, all ninety-eight pounds of her.  According to her views, she died beholden to nothing and nobody.  She was the bravest person I ever knew."