Atticus does tell Scout to learn to deal with a variety of people by looking at life through their eyes. More specifically,
"You never really understand a person until you consider things from his point of view. . . until you climb into his skin and walk around in it" (30).
But Scout still argues that since she can read just fine, and Burris Ewell isn't forced to go, then she shouldn't have to go, either. In fact, she suggests that Atticus could just teach her at home like he was taught at home. He says no because he has to make a living.
Atticus addresses the Ewell problem by telling Scout that the community bends the law in some cases because the Ewells are a special case. Since their father doesn't take care of the kids like he should, they become unmanageable and unruly. Not only that, but Bob isn't cited for hunting out of season because it's the only way the children are fed besides rummaging through the dump. Scout, on the other hand, can and should go to school and follow the law because she has more privileges and opportunities to do so. Because of this, she is held accountable to all of the laws of the land and therefore must go to school.
As compromise to settle her mind about Miss Caroline not wanting her to read with him at night, Atticus suggests that if Scout won't tell her teacher, they will continue to read even though they aren't "supposed" to. Therefore, Atticus settles the dispute by allowing her to read with him in secret if she will just go to school willingly.
This is the point where Atticus teaches Scout to "step into someone's skin and walk around a bit" or to see things from others' points of view. Atticus asks Scout to consider Miss Caroline's feelings--she's in a new town with a new job and she doesn't know anyone or any of the customs. He tries to get Scout to understand the first day of school is difficult for MIss Caroline as well.
Atticus also makes Scout a deal: they'll keep reading the newspaper at night as long as Scout agrees to keep going to school. Very quickly, Atticus teaches his young daughter the adult concepts of empathy and compromise.