Jem does not change gender. Try reading the passage. You might be confused in who is narrating. Scout, a young girl, is the narrator, not Jem, though he is an integral character. I have read the novel dozens of time and am not aware of any sort of error regarding this.
Gender roles, though, is a theme in \"To Kill a Mockingbird.\" Scout is a classic tomboy - beating up her classmates, attempting to seal a bargain with Atticus by spitting in her palm, swearing, and so on. One key thing to watch as you read is how Scout attempts to fit into the feminine world around here. This begins when her Aunt, Alexandra, moves in with the Finches. In Ch. 24 there is the great scene where Scout is helping out at an afternoon lunch with Alexandra and her friends. Scout is dressed in a skirt. One of Alexandra\'s friends asks her where her pants are. Scout promptly pulls up her skirt and shows that she has pants on underneath! This scene illustrates the conflict between her tomboy ways and the pressure to conform to the female world of behaving properly, gossiping, having dinners, and obeying traditions.
Jem faces the pressures of growing up and becoming a man. The catalyst, I believe, for Jem\'s change is the Tom Robinson verdict. Before the verdict, Jem is naive and idealistic. After that, though, his innocence dies and he begins to see the injustices inherent in the world around him, which, of course, if part of growing up and leaving the innocence of childhood behind.