How does the antagonist in the story “The Yellow Wallpaper” by Charlotte Perkins Gilman contribute to the story’s overall meaning?

The answer to this question depends upon whom one defines as the antagonist of Charlotte Perkins Gilman's "The Yellow Wallpaper." Therefore, there are two distinctly different answers. Prior to defining who the antagonist is, one must first answer the question of the story's overall meaning.
The message of the text is one which addresses the oppression of women. Here, the protagonist is unable to show her independence.
In regards to the identification of the antagonist, one could define John, the protagonist's husband, as the antagonist. By doing this, the conflict which exists is identified as external conflict and, more specifically, man versus (wo)man. Therefore, in order to illustrate how John acts as the antagonist and his character contributes to the overall meaning of the story, one must examine how John oppresses his wife. John's oppression over his wife comes in the form of his forced isolation of her from the rest of the world. She believes her home to be haunted, yet John dismisses this belief in things which "cannot be felt and seen and put down in figures." Therefore, he keeps her locked away (in her bedroom) from others. Another way he oppresses her is by ignoring the fact that she believes herself to be sick. Because of his position as a doctor, and the fact that she suffers from a "temporary mental depression," John's professional opinion is all that matters. According to him, she knows nothing of her illness or maladies. She is simply a weak woman who knows nothing.
Another plausible antagonist is defined through another external conflict (man versus the supernatural). The narrator believes that a woman lives under the wallpaper in her bedroom. No one else can see the woman, only the narrator (whom some refer to as "Jane"). While one could leave the conflict as this—a simple identification of a ghost—one could go further and state that the true antagonist is mental illness.
Some critics state that "Jane's" illness was postpartum depression. Although postpartum depression was first diagnosed in the 1850s, there was still a lack of solid knowledge at the time of the text (1892), and many did not understand the disorder.
This said, one could connect the idea of the oppression of women to the antagonist of mental illness based upon the fact that, for years, many women's illnesses were dismissed because they (women) had a long history of being seen as emotionally disturbed and difficult. "Jane's" oppression comes in the form of the strong stereotypes helped by society at large regarding mental illness. Therefore, as time goes by, she falls deeper and deeper into depression and mental instability. As she falls, the woman under the wallpaper, her PPD, becomes more aggressive and predominant in her life. The antagonist, therefore, wins, and "Jane" slides further and further into mental darkness.