Find reasoning for why Atticus is courageous.

Different readers will likely find slightly different reasons for why Atticus Finch is a brave and courageous character.  For me, two things stand out more than anything else.  
I think the most courageous thing that Atticus does is take the Tom Robinson case.  Atticus is a good and experienced lawyer.  He knows full well that he is likely to lose the case, but that's not the only reason taking the case is courageous.  By taking the case, Atticus is risking his reputation and good standing in the community.  He's even putting himself at risk of physical harm.  People could very well do harm to Atticus (or his family) for no other reason than because he is the man defending someone whom everyone assumes is guilty.  
The other courageous act that really stands out to me is when Atticus decides to go to the jail and wait for the lynch mob to show up.  

A long extension cord ran between the bars of a second-floor window and down the side of the building. In the light from its bare bulb, Atticus was sitting propped against the front door. He was sitting in one of his office chairs, and he was reading, oblivious of the nightbugs dancing over his head.

Atticus knew that putting Tom in that jail was a bad idea, and Atticus knew that people would make an attempt on Tom's life in order to get their own sense of justice.  He went to the jail in order to protect Tom from the lynch mob.  He had to have known that he wasn't likely going to be able to hold them off on his own.  He had to have known that reasoning with them wasn't likely to be successful, and he had to have known that he would have lost any kind of physical fight against a group that far outnumbered him.  It took a great deal of courage for him to stand up for what he knew to be the right thing, even in the face of physical harm.  Fortunately, Scout and Jem showed up, and Scout was able to convince Mr. Cunningham to go home.  

Atticus said nothing. I looked around and up at Mr. Cunningham, whose face was equally impassive. Then he did a peculiar thing. He squatted down and took me by both shoulders.
“I’ll tell him you said hey, little lady,” he said.
Then he straightened up and waved a big paw. “Let’s clear out,” he called. “Let’s get going, boys.”