How is Jo rebellious? How does she rebel against gender norms? How is she "breaking the rules" about being a female in this time period?

Jo is rebellious against the typical female gender role of the Civil War era because she rejects most of the norms established for proper female conduct. For one, she resents her femaleness and longs to be able to leave home and do exciting things like go to war or live in the big city (she actually does achieve the latter after she rejects Laurie's marriage proposal). She is not romantic, and rebuffs Laurie's advances for...

Jo is rebellious against the typical female gender role of the Civil War era because she rejects most of the norms established for proper female conduct. For one, she resents her femaleness and longs to be able to leave home and do exciting things like go to war or live in the big city (she actually does achieve the latter after she rejects Laurie's marriage proposal). She is not romantic, and rebuffs Laurie's advances for quite a long time before he eventually asks her to marry him; again, going against the typical female role, Jo turns him down when almost everyone expects them to end up together. 

In order to get some distance, she moves away to pursue her dream of becoming a writer. Even this is made more difficult as a result of Jo's gender; she is initially rejected by editors because she is a woman, and it takes a great deal of time for her to be accepted as a female writer of serious works. 

Jo even has what sounds like a boy's nickname, and she prefers books to music, knitting, or other more properly female activities. When Marmee needs money, Jo's pride will not allow her to ask Aunt March, so she cuts all her hair and sells it! This is certainly not "proper" behavior for a girl, and she must live with her boyish haircut until it grows out.