The word that seems to set Jem off during his conversation with Scout concerning Miss Gates is "courthouse." Jem seems calm and rational when Scout questions him about her teacher, and Jem claims to have "liked her when I was in her room." But when Scout mentions the conversation she had overheard between Miss Gates and Miss Stephanie on the courthouse steps,
Jem was suddenly furious... "I never wanta hear about the courthouse again, ever, ever, you hear me?" (Chapter 26)
Jem was still upset about the result of the trial and what he perceived as an unjust jury verdict. The mention of "courthouse" only reminded him of the trial, and Atticus explains to Scout that Jem "was trying hard to forget something"--the jury's guilty verdict that led to Tom's incarceration and death--and that he "would be himself again when enough time had passed for him to "sort things out."
The above answer is good, but more context is important. Jem and Scout are both furious at Miss Gates, but for different reasons. Scout is angry at Miss Gates, because Miss Gates does not see something very clearly. In other words, she has enormous blind spots. She is able to see that Hitler is an evil leader because he persecutes the Jews, but she is not able to see how those of Maycomb persecute blacks - especially in the case of Tom Robinson.
Here is what she says in class. Her blindness is clear as day.
We said it. Then Miss Gates said, “That’s the difference between America and Germany. We are a democracy and Germany is a dictatorship. Dictator-ship,” she said. “Over here we don’t believe in persecuting anybody. Persecution comes from people who are prejudiced. Prejudice,” she enunciated carefully. “There are no better people in the world than the Jews, and why Hitler doesn’t think so is a mystery to me.”
What makes her blindness even greater is that Scout, a mere child, sees her inconsistency.
Jem is angry when Scout mentions Miss Gates because he is reminded of the case and how ugly it was. Here is the text:
“Well, coming out of the courthouse that night Miss Gates was—she was goin‘ down the steps in front of us, you musta not seen her—she was talking with Miss Stephanie Crawford. 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. Jem, how can you hate Hitler so bad an‘ then turn around and be ugly about folks right at home—”
Jem was suddenly furious. He leaped off the bed, grabbed me by the collar and shook me. “I never wanta hear about that courthouse again, ever, ever, you hear me? You hear me? Don’t you ever say one word to me about it again, you hear? Now go on!”
For Jem, Miss Gates represents the sheer racism of the town. For this reason, Jem is angry.