At the time The Awakening was published women were expected to behave in a certain way. Women were supposed to be demure, submissive, subservient to their fathers and husbands. Patriarchal society determined that a woman's place was in the home, and that her primary duty in life was to be a loving, supportive wife and mother.
Given this restrictive cultural background, we can see just why The Awakening was so hugely controversial when it was first published. Edna Pontellier, the story's protagonist, openly defies convention by seeking to break free from a dead-end marriage. As a married woman, Edna's expected to remain faithful to her husband. But Edna feels so trapped in her loveless marriage that she embarks upon not one, but two affairs, each time with a man she claims to love. This would've been considered rather scandalous behavior at the time. Respectable middle-class women like Edna simply didn't do that sort of thing; and even if they did, many of society's self-appointed moral guardians certainly didn't think that it was a fit subject to write about.
The book's critics—many of whom hadn't actually taken the trouble to read it—also took exception to Edna's dabbling in art. Although there were of course women artists at that time, art was still generally considered to be an exclusively male preserve. The idea of a middle-class married woman expressing herself through art as Edna does was considered at best ridiculous, at worst faintly scandalous by late nineteenth-century society. Edna's artistic awakening is, in its own way, every bit as transgressive, every bit as challenging and threatening to the norms of bourgeois society as her sexual awakening.