Scout and Jem are being raised by Atticus as a single parent, because their mother died shortly after Scout was born. Since Atticus is a man, a single parent, and older than most of their friend’s parents, they are sometimes dissatisfied with him.
Atticus is not your typical father. His parenting style is rather hands-off, but he treats his kids with respect and wants them to grow up with a strong moral code.
Jem and I found our father satisfactory: he played with us, read to us, and treated us with courteous detachment. (ch 1, p. 3)
The words “satisfactory” and “courteous” are not what you’d expect in a discussion of a parent, let alone “detachment.”
Atticus was never too tired to play keep-away, but when Jem wanted to tackle him Atticus would say, "I'm too old for that, son." (ch 10, p. 64)
The children are convinced that their father is not special. He does not have a job they appreciate, so they think he doesn’t do anything.
Scout in particular gets very confused when children and even adults mock Atticus’s defense of Tom Robinson. Since people are so angry at him, she wonders why.
"Do all lawyers defend n-Negroes, Atticus?"
"Of course they do, Scout."
"Then why did Cecil say you defended n-s? He made it sound like you were runnin' a still." (ch 9, p. 53)
They do not really understand what he does until they see him in action at the trial. After the trial, Scout and Jem are no longer ashamed of Atticus. It is during the trial that they realize how important what he did was. He sacrificed himself and put himself at risk for the sake of the town, which is much more courageous than shooting a mad dog.
Atticus is older than most parents of Scout's friends. Scout and Jem talk about Atticus not being able to do anything -- meaning that he's too old to play games with them like most dads. She is naively under the impression that because he doesn't show off any particular skills, he must not have them. This misunderstanding is resolved when Atticus shoots the rabid dog, and it is revealed the Atticus is possibly the best shot in the county (Chapter 10). Scout realizes that her father has skill with a gun, but that he only uses it when necessary because he feels he has an unfair advantage over animals. This revelation not only gives Scout a renewed respect for Atticus, but also helps develop the theme of innocence in the novel.