theme associated with the title.  "The Mockingbird" that it is a sin to kill symbolizes the person who is defenseless, who is "killed" either literally or symbolically by society.  Atticus is the great defender of the the mockingbirds or the defenseless souls in the novel.  Mrs. Dubose was a victim of society because soceity tends to label people as mean or spiteful without knowing what internal demons they are fighting.  She was fighting a drug problem the hard way, by quitting on her own.  Yet, no one except Atticus bothered to consider this. This proved that she was brave and a good person.  Like Mrs. Dubose, Tom was also defenseless.  Atticus knew that he wouldn't win the case, but he defended Tom to the best of his ability even though the town made him and his children miserable because of it.  He did it for the same reason that he made Jem read to Mrs. Dubose, because they were victims of society who had no one else to defend them. Because Tom was black, society convicted him before he ever stepped into the courtroom.  Even after Atticus proved he could never have hurt Mayella, the jury still sentenced Tom to death.  Like the mockingbird, they had no chance of surviving in an unjust world.

Atticus feels that Mrs. Dubose is a great lady because she is strong-willed and proud, and lives life on her own terms.

Mrs. Henry Lafayette Dubose is the neighbor whose house is two doors to the north (Ch. 1).  She is described as “plain hell” and “the meanest old woman who ever lived” (Ch. 4) and is a fixture in Scout’s childhood.  For most of the time Scout is growing up, Mrs. Dubose is just there, yelling insults at the children as they pass by even if they attempt to be nice to her.

Atticus is always polite to Mrs. Dubose, despite her rudeness.  He is polite to everyone.  The encounter Jem has with Mrs. Dubose’s flowers gives Atticus an opportunity to teach his children responsibility, but after her death he also lets them know why he considers her such a courageous person.  After Jem destroys her flowers, Atticus has him go to read to her.  He later explains that he wanted his children to see what real courage is.  Sometimes courage is mental as well as physical.

Mrs. Dubose was addicted to painkillers, and she wanted to wean herself off of them before she died.  She was having Jem read to her so that she could have a distraction.  Jem did not know any of this until later, but Atticus knew that he could explain it and Jem would understand.

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. (Ch. 11)

Mrs. Dubose was an underdog.  She was addicted to morphine, but she kicked the habit.  What she did took immense courage.  Atticus wanted his children to see that sometimes you can win an unwinnable fight, and sometimes just trying to win when it seems impossible is courageous.  Atticus himself was facing an uphill battle that would require courage of him and his children as the trial began.  Showing them Mrs. Dubose was a way of sending a message about different types of courage, and courage being found in the least expected places, to encourage them to find it in themselves.

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."

You would think it would be pretty strange that Atticus would say this about Mrs. Dubose.  After all, she pretty much stands for everything he hates.  She is so horribly racist and she is willing to abuse Atticus's own family because of his stands on racial and other issues.

But Atticus admires her anyway because of the way she fights off her morphine addiction in the month or so before she dies.  He respects her determination and her bravery.  This is why he says she is a great lady.  He says that courage is the determination to get back up again even though you know you're "licked."

Atticus has a genuine respect for the people around him, even when their behavior perhaps does not justify his high regard.  The reason he thinks so highly of Mrs. Dubose, he tells the kids, is that she could have continued with her morphine to keep herself comfortable as she died, but she was adamant that she would "leave this world beholden to nothing and nobody".  Because Atticus has such admiration for a woman as stubborn and determined as Mrs. Dubose, it is completely consistent with his character that he would defend Tom Robinson; like Mrs. Dubose, Atticus is not one to shy away from a fight, even if it becomes unpleasant.  He knows the road ahead is going to be difficult, long before the trial even begins, warning Scout and Jem to remember that regardless of what the townspeople say about Atticus, Tom Robinson, and the case, the Finches will still consider them friends. 

Although Atticus is loyal to his friends, the people of Maycomb, he is absolutely determined that he will give Tom Robinson the best defense he possibly can, and on the topic of people falsely accusing and taking advantage of people who are black, he does not mince words.  While the term "trash" is freely thrown about Maycomb to describe nearly anyone who doesn't fit into the narrow definition of non-trash that the people have established, Atticus doesn't normally use that term, except when he tells Scout and Jem the following: 

As you grow older, you’ll see white men cheat black men every day of your life, but let me tell you something and don’t you forget it—whenever a white man does that to a black man, no matter who he is, how rich he is, or how fine a family he comes from, that white man is trash.

Atticus said that Mrs. Dubose was a great lady because she was struggling to overcome a debilitating addiction, and she decided to do it cold turkey, alone, at the end of her life.  She wanted "to leave this world beholden to nothing," and so decided to break her morphine addict.  He said that she demonstrated true courage, which was "when you know you're licked before you begin but you begin anyway and you see it through no matter what."  And that is exactly what Mrs. Dubose did; she undertook the fight to break her habit even though the odds of really breaking it were very slim, but she did it anyway.  It was hard, very hard, but she stuck it out, and that is why she was such a great lady.

This relates to Atticus taking the Tom Robinson case, because he knew when he took it that he probably wouldn't win it.  But, he took the case anyway, just like Mrs. Dubose decided to kick her habit anyway.  And, Atticus saw it through no matter what-even though people were mocking his children, even though an angry mob showed up at his door, even though a mob showed up at the jailhouse, and even though it set many people in the town against him.  He did it anyway, and kept going, even though he knew that he probably wouldn't win it.  So, Atticus fits his own definition of courage that he had originally applied to Mrs. Dubose.  He starts a battle he can't win because it is the right thing to do.

The kids think that Mrs. Dubose is terrible. They have their own stereotype against her because she is just mean and old. Children tend to have fears of the elderly because their aren't often exposed to the elderly and being generations apart, they don't understand what old people experience, nor can they relate to pain or generations gone by. They are prejudiced toward her.

The town has a prejudice for Tom Robinson. Clearly the kids are coming to understand that as they experience more and more comments from adults.

Atticus wants the children to understand that you don't pick and choose who you defend when you are a lawyer. Atticus sees people as inherently good. He can certainly find flaw with folks, but he forgives their flaws. He chooses to focus on the good. Atticus truely believes in Tom and trusts the testimony that Tom is preparing to be truth. Atticus' knows Tom is a good man. He is trying to help the kids see that we can't judge people based on our own bias. Their bias against Mrs. Dubose is only founded on their experiences with her that were in the end of her life and often influenced by pain. Atticus had a broader life experience from which to choose for drawing his perceptions of her.