Why does Mayella start to cry in court in To Kill A Mockingbird ?
This is a good question. Mayella Violet Ewell takes the stand in chapter 18. As soon as she comes up, she starts to cry. Judge Taylor allows her to cry for a while. Afterwards, he tells her that she has nothing to fear. As she continues to cry, Judge Taylor asks of whom she is afraid. She points to Atticus. She explains that she does not want to be treated in the way her father was treated by Atticus on the stand. Here is the dialogue and description:
Mayella said something behind her hands. “What was that?” asked the judge.
“Him,” she sobbed, pointing at Atticus.
She nodded vigorously, saying, “Don’t want him doin‘ me like he done Papa, tryin’ to make him out lefthanded...”
Judge Taylor scratched his thick white hair. It was plain that he had never been confronted with a problem of this kind. “How old are you?” he asked.
Now to the answer to your question. Mayella is afraid of Atticus and this is why she starts to cry. She probably realizes that Atticus is an intelligent man and that she is lying. So, her lie might be exposed by the sheer logic of Atticus' examination.
When she mentions the left hand bit, she is referring to Atticus's intelligent observation that Bob was left-handed, which would explain the bruises on Mayella's face only on the right side.
She is also afraid because she is a young girl and she has never been the center of attention.