What reasons does Scout give for why she doesn't need to go to school? Is Atticus convinced by them?

Scout tells Aticus that she wants him to teach her at home before finally sharing that Miss Caroline said he couldn't teach her at home anymore. Atticus is not convinced and explains that she needs to put herself in Miss Caroline's shoes, as she had learned a few lessons that day as well.

“You never went to school and you do all right, so I’ll just stay home too. You can teach me like Granddaddy taught you ‘n’ Uncle Jack.”

Bit by bit, I told him the day’s misfortunes. “-and she said you taught me all wrong, so we can’t ever read any more, ever. Please don’t send me back, please sir.”

Atticus said I had learned many things today, and Miss Caroline had learned several things herself. She had learned not to hand something to a Cunningham, for one thing, but if Walter and I had put ourselves in her shoes we’d have seen it was an honest mistake on her part. We could not expect her to learn all Maycomb’s ways in one day, and we could not hold her responsible when she knew no better.