In Kate Chopin's short story, Louise Mallard is described as "young, with a fair, calm face, whose lines bespoke repression and even a certain strength." She has, evidently, experienced repression as part of her Victorian-era marriage, one in which she has few legal rights because her husband is entitled to act on her behalf, to make decisions for her, and so on. Brently Mallard has always been a good and loving husband; even Louise reflects and knows that "she would weep again when she saw the kind, tender hands folded in death; the face that had never looked saved with love upon her [...]."
Brently is not the problem here; the institution of marriage seems to be the problem. That is what Louise takes issue with, not the man himself. He seems always to have loved her and to have acted as husbands were supposed to act at the time. However, even Louise's (uneven) love for him cannot hold a candle to "this possession of self-assertion which she suddenly recognized as the strongest impulse of her being!" She needs to be free—and freedom for marriageable upper-class women in this era could really only be gained by widowhood. One would have done one's duty, so to speak, and could live comfortably as a widow for the remainder of her days.
The authority-figure, perhaps the girl's mother, in Jamaica Kincaid's piece, also seems to mean well. She is doing her best to educate the girl, perhaps a daughter, in the ways of the world and the kinds of work that women are supposed to do. However, this care and concern also feels repressive, just as marriage feels repressive to Louise. We see the desire for freedom, at least freedom of identity, in the girl's speech, in italics, "but I don't sing benna on Sundays at all and never in Sunday school." She protests and tries to ask questions, trying to find a space for her self amid all these rules.
Both Louise Mallard and the titular girl chafe against the social expectations of women, in whatever condition of life they find themselves. Both seem to long for freedom—to be autonomous and to have their own identities despite all of the rules—and both have their freedoms repressed by some well-meaning person in their lives.