On what single issue did Atticus build his case? Why did Mayella resent Atticus?

I think if you have to sum his case up in one word, you
could say injury. Mayella's injuries were the focus of every testimony. Of Bob and Heck,
he asked about if anyone ever called a doctor. He wanted an answer to this question
because it could have provided another layer of evidence. It also would have shown a
seriously concerned father. His lack of regard for her injuries shows a disrespect for
his daughter. Her testimony focuses on where her bruises were and what was done to
her... in her words. Tom's testimony then demonstrates his inability to inflict these
injuries.

Mayella didn't like Atticus for pointing out the
truth. There was not any trickery, just cold hard factual evidence. She thought his
courtesy was rudeness. That just demonstrates how out of touch she was with
society.