Because everyone in the town knew he was lying. Atticus took that harrasment/beating to save mayella from a beating at home.
Boo Radley saved the children from Bob Ewell. Atticus thanks Boo because if Boo hadn't stepped in to stop Bob Ewell, the children probably would have been killed. Atticus is thanking Boo Radley for keeping his children alive. At least, that's how I see it :)
Atticus explains to Scout that using the word "nigger" is disrespectful and offensive because it is a derogatory term used to dehumanize African Americans. He teaches her to treat everyone with respect and kindness regardless of their background or race.
The children thought Atticus was too old because he did not participate in physical activities like their friends' fathers did, and his hair was turning grey. In addition, Atticus was more reserved and calm compared to the other fathers in the town.
Because Atticus thought there were more important things to be proud of their father than of shooting a gun.
Atticus shoots the mad dog almost perfectly in the forehead. His children were awestruck. Atticus used to be called ol' one shot, but his kids never knew he had even picked up a gun. He was labeled the deadest shot in Maycomb County.
Atticus thinks they didn't stay because scout has a blanket wrapped around her shoulders.
Bob after the trial threatens Atticus that he will shoot him. Bob Ewell feels a lot of anger towards Atticus because Atticus humiliated Bob Ewell in his first time in court. Although Bob Ewell did win the case he lost a lot of his little pride he had.
Mayella's reaction to Atticus' behavior in court is ironic because Atticus is the only person actually trying to defend her and seek justice for her, yet she is hostile towards him. Despite his efforts to help her, Mayella feels threatened by Atticus' questioning and sees him as an enemy due to her prejudiced views.
Because she could have a feminine influence on the children.
Aunt Alexandra asks Atticus to explain the children because she disapproves of their behavior and wants Atticus to instill in them a sense of proper behavior and manners. She believes Atticus should be more authoritative and involved in their upbringing.
Calpurnia (the Finches' housekeeper) brings a note telling Atticus that Scout and Jem are missing. Soon after, however, Mr. Underwood tells Atticus that the children are in the courtroom in the colored balcony.
When Aunt Alexandra tells Atticus that the children shouldn't have seen the trial of Tom Robinson, Atticus responded that it was important for them to see it and learn from it. He said that they needed to see the ugliness of their society, as well as the good, in order to have a balanced adult perspective.