Gender Roles and the "New Woman"
The 1920s brought massive changes for women, and you can see both progress and limitations in Gatsby's female characters! The era introduced "flapper girls" with short skirts, bobbed hair, makeup, and a spirit of independence. These exciting and glamorous distractions offered themselves to the "new woman" who wanted financial independence and free will.
However, competition exists everywhere - between men and women, and even among women themselves (Daisy, Myrtle, and Jordan all compete for status and attention). Traditional expectations still demanded that women raise children and keep house, but these demands became less compatible as women began rebelling against authority.
Daisy, Jordan, and Myrtle represent different responses to these changing times. Jordan shows assertive attitudes and belongs to a class of women not expected to be self-sufficient. Myrtle demonstrates the power women could wield (though Tom criticises this), whilst Daisy remains trapped between old and new expectations, viewed as both beautiful and bewildered.
Important insight: The patriarchal society moulded women to think they couldn't empower themselves - they still needed men's money and protection to survive.