why does scouts ability to read and write annoy her teacher,miss caroline?
Miss Caroline Fisher is a weak, inexperienced teacher. As such, she appears insecure in her abilities. So when Scout shows up for her first day at school, and is clearly able to read and write, Miss Caroline gets quite indignant. Atticus must've taught her, she thinks. And Miss Caroline feels rather put out as she seems to think it somehow undermines her authority as a teacher.
The unpleasant episode with Miss Caroline illustrates once more the warped nature of life in Maycomb. It's perfectly fine for Burris Ewell to turn up for the first day of school and then stay away for the rest of term. But for a child to come to school with the ability to read and write is somehow a problem. Clearly, it's more important to follow strict, inflexible rules than to educate children properly. Miss Caroline is one of many adult authority figures in the story whose actions make little sense to those of us not familiar with the strange customs, laws, and conventions that govern the lives of the citizens of Maycomb.