A great example of a quote that shows how fair Atticus is as a father, and as a listener, is found in chapter 9. It is the winter holiday season, and Uncle Jack, Aunt Alexandra, and Francis, come to visit the finches. Scout cannot stand Francis, and has been planning to do something to him. When she cusses at him, her uncle comes by and spanks her. This is a shock to Scout, because Atticus is much more democratic with his children, always willing to listen to each one.
"When Jem an' I fuss Atticus doesn't ever just listen to Jem's side of it, he hears mine too"
Yet, throughout the novel Atticus displays fairness, over and over. He calmly listens to Scout's angry rants against her school and teacher. He also calmly corrects Scout in the usage of the "n" word. He is all ears when Jem shows his anger at the justice system, and he is even willing to put into perspective the presence of his children at the Cunningham lynching attempt. He puts his own fatherly fears to the side and even commends Scout in changing Mr. Cunningham's mind about the attack on Tom Robinson.
Another important moment, this time with Miss Maudie, Scout explains how Atticus (as shown in the examples before) is adamant in running his household and his children in a formulaic way, as it occurs in the courtroom. Everything has a protocol, a process, and an order. In the same token, Atticus is also quite transparent in his discipline techniques. He would never to do the children "inside the household what he don't do in the yard". This means that if Atticus ever has to correct his kids he will do it instantly and after having heard both sides of the story. This is demonstrative of Atticus's strong backbone despite the doubts of some people in town.
Atticus is an understanding father because he listens to his children. He seems to care how they feel and what they worry about.
When Uncle Jack spanks her for swearing at her cousin, Scout lectures him on Atticus’s theory of child-rearing.
When Jem an' I fuss Atticus doesn't ever just listen to Jem's side of it, he hears mine too… (ch 9)
Fairness is very important to children, and this is one way that Atticus is an understanding father.
Atticus also does not beat his children, although he often threatens to do so. Uncle Jack is shocked to hear this. Atticus explains.
[Scout] minds me as well as she can. Doesn't come up to scratch half the time, but she tries. (ch 9)
Perhaps the best evidence that Atticus is an understanding father is that the children come to him for advice. He is more interested in talking to them and getting to the bottom of the problem than he is in punishing them. In this way, he can teach them strong moral lessons and they become better people.