How does Rachel’s visit to Bert create conflict between the two?

When Rachel visits Cates in jail, she brings him a clean shirt, tie, and handkerchiefs. She asks him to admit he was wrong and say the lesson was a joke, figuring if Matthew Harrison Brady ­ "the biggest man in the country ­ next to the President, maybe" ­ is coming to town to say he is wrong, then he must be. Cates says that all he did was teach Chapter 17 in the biology book, Darwin's Origin of Species. Rachel insists that everyone says that what he did was bad, and that there's a law against it, but Cates says that everything is not black and white. Nevertheless, the two embrace.

In context, we can see that Rachel is buckling to public opinion, and Cates was defending his actions.