Mrs. Gates' hypocrisy is introduced in Chapter 26, during a lesson on Current Events. In class, Cecil Jacobs gives an overview of Hitler's treatment of the Jews: "Well anyway, Hitler's started a program to round up all the half-Jews too and he wants to register 'em in case they might wanta cause him any trouble and I think this is a bad thing and that's my current event."
When asked how Hitler could do such a thing, Miss Gates seems delighted at the opportunity to explain the difference between a dictatorship and democracy. Yet it's also a chance for her to expose her own hypocrisy. "Over here we don't believe in persecuting anybody. Persecution comes from people who are prejudiced." In response to Cecil's question about why the Jews are persecuted--(here Dill includes the ironic comment, "They're white, ain't they"?)--Miss Gates adds that the Jews' persecution since the beginning of time is "one of the most terrible stories in history."
Scout muses over this, thinking that Hitler should probably be the one put in a pen. But something else troubles her: "There was something else wrong--I would ask my father about it." She approaches Atticus tentatively and asks whether it's right to hate Hitler or not, also mentioning how angry Miss Gates got about Hitler. Yet she is unable to proceed with her question, uncertain that she could put her feelings into words for Atticus.
Instead, Scout goes to Jem because he "understood school things better than Atticus." When she mentions to Jem that Miss Gates hated Hitler a lot, Jem cannot at first comprehend her point, until she recounts something she overheard on the courthouse steps.
Here Scout gets to the heart of her confusion: she mentions that she observed Miss Gates and Miss Stephanie Crawford making hateful remarks (it is clear that the remarks refer to the Negroes in Maycomb). "I 'I heard her say it's time somebody taught 'em a lesson, they were gettin' way above themselves, an' the next thing they think they can do is marry us.' "
Scout wonders aloud how a person can hate Hitler then "turn around and be ugly about folks right at home--." Neatly pointing out Miss Gates' hypocrisy this way makes Jem so furious that he grabs her and warns her never to talk about the courthouse again. Surprised, Scout retires to the comfort of Atticus' arms. Atticus knows that Jem is "having a rough time these days," that is he "trying hard to forget something...storing it away for awhile" until he could understand it better. We know that it's the trial he is trying to forget.
The contrast in the siblings' behavior can be owed to their ages: while young Scout has merely perceived Miss Gates' hypocrisy, Jem has the maturity not only to understand it, but to let it move him to fury.