Jane's (the narrator's) husband and brother are physicians. She believes that the best thing for her condition is to work and have some excitement in her life. But her brother and husband tell her that she needs to take certain medications and avoid work. She accepts their verdict because they have the authorial position of being physicians and because they are men. She must share her thoughts only with pen and paper. She is forced to hide her own thoughts. "I did write for a while in spite of them; but it does exhaust me a good deal -- having to be so sly about it, or else meet with heavy opposition."
Her husband, John, says the worst thing she can do is think about her condition. In other words, he will do the thinking for her. This shows how the husband makes all decisions for the wife. She is clearly in an inferior position and reluctantly accepts this dynamic because these are traditional male and female roles.
The fact that Jane must hide her writing is significant. John forbids her from even thinking about her condition. He treats her like a child. He certainly doesn't want her to put her thoughts on paper. John's idea is to close her up in the room in the house, keeping her from any engaging activity. It is like a prison sentence. She feels closed in, isolated, and this leads to her having a breakdown.
When Jane hallucinates about the woman trapped in the wallpaper, she is envisioning her own trapped feelings. At the end of the story, it is Jane who has escaped from the wallpaper. This is symbolic. It shows her desire to escape from that room and from her traditional female role which is subservient to the male, John. "I've got out at last," said I. "in spite of you and Jane? And I've pulled off most of the paper so you can't put me back!"