What does Jem say that shows he learned courage at the end of Harper Lee's To Kill a Mockingbird?

Throughout Harper Lee's To Kill a Mockingbird, Atticus equates being courageous with being a gentleman. By the end of the novel, Jem shows he also understands the connection between bravery and courteous behavior when he tells Scout not to squash a roly-poly bug.

Jem first understands his father's philosophy of associating courage with courteous behavior when he apprehends why Atticus kept his sharpshooting skills a secret. As Miss Maudie explains, Atticus gave up shooting because he realized his expert marksmanship placed him at an "unfair advantage over most living things" (Ch. 10). Yet Scout, being young, still has difficulty understanding why Atticus isn't proud of his sharpshooting skills and why he hesitates to kill living things. Jem, on the other hand, understands that both Atticus's refusal to boast about his skill and hesitancy to kill is because, as Jem exclaims, "Atticus is a gentleman, just like me!" (Ch. 10). In other words, Atticus neither kills nor boasts about his ability to kill because he believes in being gentlemanly, or courteous, towards all living things. Since most of society doesn't hold the same views about killing and boasting, it takes a great deal of courage to always respect life and behave courteously.

Later, Atticus further demonstrates courage by addressing Mrs. Dubose in a gentlemanly manner, despite her own ill manners. Even his ability to see Mrs. Dubose's value as a courageous person herself demonstrates his own ability to act with courage. It takes a great deal of courage to always be respectful and find the value in others, especially when the rest of society is disinclined to be respectful and value others. By the end of the novel, we see that Jem has taken these lessons of demonstrating courage through respecting and valuing others to heart.

In Chapter 25, soon after Tom Robinson is shot to death by prison guards, Jem demonstrates his lessons of courage by telling Scout, just as she is about to squash a roly-poly bug after playing with it, "Don't do that, Scout. Set him out on the back steps," and by further explaining, "... they don't bother you." Jem's protection of the roly-poly directly reflects his father's lesson concerning it being sinful to kill innocent things and his lesson concerning respecting and valuing others. Hence, the moment Jem commands Scout not to kill the bug is the moment he says something that most demonstrates the lessons of courage he has learned throughout the book.