Consider first, the primary characters whose mothers are absent: Scout/Jem, Dill, Boo Radley, and Mayella Ewell. Not much is known about Mayella's mother, except that in her absence, Mayella takes over many maternal duties including watching the children. The absense of Boo's mother heightens the mystery and strangeness of the Radley family for the neighborhood. The primary reason for Dill's absent mother is to give a reason for his staying at Aunt Rachel's house every summer (and as a point of fact, because Dill is likely based off the real life friend of Harper Lee: Truman Capote). And finally, Scout's absent mother is not necessarily a focus of the book, except to heighten Scout's tomboyishness. Calpurnia, Aunt Alexandra, and Miss Maudie all play maternal roles in Scout's life, and Atticus is a better-than-average single parent.
The best evidence for the idea of "abusive fathers" in the book comes from Bob Ewell and his alleged treatment of Mayella (which turns into the Tom Robinson trial). Again, the focus here is Tom's innocence, and Atticus' role in the trial. The abuse of Ewell toward his daughter is secondary and a minor focus in the scope of the novel. There may be evidence to support that the Mr. Radley's (both Boo's father and Nathan, a father-figure) are abusive toward Boo, but it would be a bit of a stretch. Perhaps Boo Radley and Dill could be put together in a category of abuse by neglect. In a way, each of these characters' relationships with their fathers seems to directly contrast the healthy and loving relationship of Atticus with his children. Scout manages to find a connection with each character despite their differences, however.
The first absent mother would be the mother of our main character Scout Finch. She died when Scout was two, so she never knew her. However, growing up in an era when girls wore dresses and practised their manners on a daily basis, it is obvious that Scout did not have a female influence around the house. Scout did have Calpurnia around to help keep her in line, though, unlike our other motherless character.
Mayella Ewell had no female influence whatsoever. No word is ever mentioned about her mother or where she was. Instead, she was in charge of seven other children/siblings and a father who was drunk most of the time. Because of her lack of female influence, Mayella gets herself into a mess of trouble by tempting a Negro and then accusing him of raping her when she gets caught trying to kiss him. Instead of coming clean, Mayella only proves to the court how pathetic her life really is, and continues to point her finger at Tom Robinson.
The other theme dealing with parenting is the theme of abusive fathers. Boo Radley's father was the first one introduced. Although not physically abusive, he forced Boo to remain indoors for the rest of his life, turning him into a recluse and the town Bogeyman. We finally get to see what time and distance from others has done to Boo when we get a glimpse of Boo in the final chapters.
The last abusive father is Bob Ewell. He abuses Mayella physically. In fact, Atticus proves that Bob is responsible for the injuries she blames on Tom. Without a woman around, Bob not only abuses Mayella physically, but also sexually. In Tom's testimony he says that Mayella told him "what her papa do to her don't count."
With these two themes, the contrast is made between the type of fathers these men are to the kind, responsible character of Atticus. Alone, he is able to teach his children what true courage is as well as how to really understand other people. So these situations draw to light how great Atticus truly is to his children.