I think that miss Caroline is a villian, she herself caused all the troubles to befell her, due to her rigidness and unwillingness to change.
During the first day of school, when she called scout up to read, she found out scout was illiterate. She reacted with distaste, and stopped scout from learning to read at home. This showed that she follows her plans unconditionally, and if anything interrupts her plans, she would stop it. Because she thought that she was employed to teach scout to read, and if scout is already capable of reading, then what's the point of her there? This showed her rigidness. Because she is rigid, she did not want to change her teaching methods when she went to may comb, a different society compared to Alabama. This caused the students to be distracted and unable to focus, thus causing her a lot of trouble, and the worsening of her and scouts relationship. As showed with the incident with Walter, lending Walter money would be perfectly acceptable in Alabama, where people were richer, but in may comb, the people are poorer, and like the cunning hams, they can't even afford the luch money. Her rigidness caused her to disregard scouts protests, and not to delve deeper into the matter. Admittedly, scouts phrasing was very disrespectful, but she should have realized that in maycomb county, most people are illiterate, and thus she should have made allowances for scout, and tried to understand the matter.
Thus, her problem stems from the fact that she is unwilling to change her teaching methods and ways when she went to a new society, and caused her to be unable to handle the class well, and caused the displeasure of other teachers as well because of the noise the class was making.
Thus, miss Caroline was a villian, because she was too rigid in her ways, and unwilling to change, which led to all the problems and hardships she faced in maycomb county.