What are some ways in which Jem loses his innocence in Harper Lee's To Kill a Mockingbird?

In Harper Lee's To Kill a Mockingbird, one way in which Jem loses his innocence is by witnessing Tom Robinson's jury deliver a very unfair verdict. The unfairness of the verdict brought Jem to tears while frequently saying, "It ain't right," walking with Atticus on the way home from the trial. Not only does the verdict enable Jem to see for the first time that evil exists in the world, such as injustice, it also enables him to see just how much people have a tendency to hate each other. Jem grapples with understanding why people hate each other as a result of his loss of innocence.

We see Jem grapple with people's hatred in Chapter 23, the day after the trial. In Chapter 23, Aunt Alexandra angers Scout by calling Walter Cunningham "trash" and forbidding her to play with him after school, and Jem leads the sobbing Scout out of the room. While in Jem's room, Scout and Jem converse about differences between people. Scout protests against the idea that there are different "kinds of folks in the world" and that those differences are marked by differences in levels of education. Instead, Scout insists that "there's just one kind of folks. Folks." Jem argues that he used to think the same way as Scout but has since needed to understand why so many people in the world hate each other, as we see in his following speech:

That's what I thought, too, ... when I was your age. If there's just one kind of folks, why can't they get along with each other? If they're all alike, why do they go out of their way to despise each other? (Ch. 23)

While Scout is correct in asserting that all people are the same, Jem is also correct in asserting that people see differences in each other, and those differences widely have to do with differences in education level. Scout's perspective shows how naive and optimistic she still is, whereas Jem's perspective shows he is developing a deeper understanding of the ways in which people treat each other. His need to come to terms with people's hatred and to find an explanation for it shows that he is no longer naively optimistic like Scout; he has instead lost his innocence due to witnessing people's hatred and its consequences.