Atticus Finch is a good father and a good man because he cares about others, no matter who they are.
Atticus is an excellent father to his two children, Scout and Jem. He reads with Scout and plays football with Jem. You can tell how much Scout loved her father, and how much time she spent with him, when she describes how she learned to read.
I could not remember when the lines above Atticus's moving finger separated into words, but I had stared at them all the evenings in my memory, listening to the news of the day, … - anything Atticus happened to be reading when I crawled into his lap every night. (Ch. 2, p. 23)
It is this same kind of gentleness that makes Atticus famous throughout Maycomb. Atticus is an unusual man. After all, he raised two children from a young age without a wife. For some reason he decided that they should call him by his first name instead of calling him “Dad.” It is not a gesture of familiarity, because they also call him, “sir.”
Atticus never lays a hand on his children. He reasons with them, teaches them right from wrong, and makes sure they have strong moral compass. He teaches them not to harm living creatures, to respect the elderly and the poor, and not to insult the neighbors. He does all of this without ever spanking them, although he threatens to wear them out quite often. When Uncle Jack, Atticus’s brother, spanks Scout, Atticus admits that he has never spanked Scout. Jem also admits to Scout that Atticus has never spanked him when he goes to get his pants from the Radley yard.
"Atticus, you've never laid a hand on her."
"I admit that. So far I've been able to get by with threats. Jack, she minds me as well as she can. Doesn't come up to scratch half the time, but she tries." (Ch. 9, p. 116)
What we see is that Atticus is really a gentle soul. He does not want to kill mockingbirds or shoot guns. He speaks politely to the mean Mrs. Dubose, talks down an angry mob, and simply wipes his face when Bob Ewell spits in it. Atticus would never hurt a fly, although he is a crack shot.
Of course, the best trait of Atticus is, as you mentioned in your question, his inclusion. He treats everyone alike. He treats his black cook, Tom Robinson, and everyone else, with dignity and respect. He talks to Walter Cunningham at the dinner table as if he were a grownup and not poor. He gives him the dignity of both an adult and someone of means. He also gives Tom Robinson the dignity both of believing him and really defending him. He even tries to convince him to go for an appeal. The wisdom of Atticus is that everyone is equal. He proved it.
But there is one way in this country in which all men are created equal. ... That institution, gentlemen, is a court. (Ch. 20, p. 274)
Atticus Finch is the type of man everyone wants for a father, and for a lawyer. He is also the man you want if there is a rabid dog coming at you. How can one man be so many things to so many people? In Atticus Finch, Harper Lee created a man who was not perfect, but was trying his hardest to be a good man, and set an example not only for his children, but for an entire town, on how to do the right thing.
Note: It is difficult to provide page numbers, because there are so many different versions of the book out there. My book will likely be different from yours. I am giving you chapter numbers and the page numbers in my book, and you can find page numbers from that.