In Chapter Two of To Kill a Mockingbird, Scout gets in trouble on her first day of school. Miss Caroline writes the alphabet down on the blackboard and asks Scout to read it out loud. When Scout is able to do so successfully, Miss Caroline reacts in frustrated disbelief and makes Scout read aloud most sections of the classroom textbook, My First Reader, and the stock-market quotations in The Mobile Register. Scout's natural ease with this task irritates Miss Caroline even further, and she demands that Scout not allow her father to teach her anything else at home since it causes "damage."

In reality, it is Calpurnia--and not Atticus--who is to blame for this trouble. To keep Scout out of her way on rainy days, Calpurnia would make her write out the alphabet and copy a chapter of the Bible underneath it, rewarding her with a butter and sugar sandwich if her penmanship was neat enough.  

You can find the answer to this in Chapter 2. What is Calpurnia's fault is the fact that Scout can write.  Her teacher does not think she should be able to read at this point and is upset that she does.

Scout says that Calpurnia is the one who taught her to write.  She says that Calpurnia taught her to write on rainy days.  She thinks that Calpurnia did it to keep Scout from annoying her too much -- she just had her sit down and work on her letters and copying passages from the Bible and other stuff like that.

What was Calpurnia's fault in To Kill a Mockingbird?

According to Scout, it's Calpurnia's fault that she's got into trouble at school. Apparently, this is because it was Calpurnia who taught Scout to read, and Scout's new teacher Miss Caroline doesn't think that's appropriate.

A young woman with very little experience of being a teacher, Miss Caroline is somewhat out of her depth. Wanting to prove that she can handle a classroom full of kids, she's anxious to assert her authority, and she feels that this authority has been undermined by Scout's already knowing how to read and write. As far as she's concerned, it's her job to teach Scout these things.

Scout has just had a fight with Calpurnia over Cal Cunningham's table manners. Scout is horrified by Cal's uncouth behavior at the dinner table, whereas Calpurnia chides the young lady for what she perceives as her snobbery.

As a result of their argument, Scout isn't in the best of moods and blames Calpurnia for getting her into trouble at school with Miss Caroline because it was Calpurnia who taught her how to read.