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.

Gender ambiguity is indeed a motif in To Kill a Mockingbird.  Atticus is not like other men in the town because he neither hunts nor plays football (much to Jem's dismay); Scout disdains all that it means to be a "lady" and wears overalls and fights; Maudie also wears overalls and live the life of a single woman.  Even Bo, in so far that he is a recluse, is somewhat "feminized" by adhering to the private rather than the public sphere.  As the novel develops, however, Atticus becomes more manly in shooting the dog; Scout becomes more feminine as she learns her place in society under the tutelage of her aunt; and Bo, in defending Jem, asserts his manhood, even though Scout reminds him of that by allowing him to "escort" her as she leads  him back to his house at the end of the novel.  As for Jem---that's interesting that you might consider some gender slippage as he becomes a gentleman. That he is unable to defend  his sister does show his vulnerability also (which is usually a position of femininity in our culture), although he also puts his life on the line to protect her.

Jem is a young boy who ages from 10 to 13 in the novel. What is probably confusing you is that Jem's changes are explained by his sister, so you're getting a female's point of view on a male character. Jem changes throughout the novel in maturity, from a little boy who never turns down a dare, to a protector of Scout, and a gentleman.