Gender inequality is a source of division in Little Women. Gender constrains the main characters in the novel: Mrs. March and her four daughters. They don't have the same job opportunities as men, although they are forced to work for a living. They also have to restrain their behavior to align with the rigid social norms of the period. This is hardest on Jo, a young woman who wishes at times she could be a man. Jo chafes at having, for instance, to sit quietly and read to her Aunt March when she would rather be outside doing something active with Laurie. The expectation of marriage also hangs over the girls and is a source of division in the second part of the novel, as Meg marries and Amy heads off to Europe and eventual marriage. But other factors divide the girls from one another, such as Beth's death and Jo moving away to better earn a living.
The dominant source of division in the novel, however, especially in the first half, is the moral failings of the girls. Marmee giving the girls each their own copy of Pilgrim's Progress as the novel opens points to this theme of moral improvement. To grow from girls to little, or what we today would call young, women, the girls have to grapple with their faults: for example, Meg is vain about her looks, Jo is impulsive and has an explosive temper, and Amy suffers from pride and being spoiled as the youngest.
Divisions between the sisters arise out of their vices. Jo, for instance, explodes in rage when Amy burns her book manuscript and rejects her, to the point that Amy, trailing after Jo and Laurie as they ice skate, falls through a patch of thin ice and almost drowns.