In Kate Chopin's story "Desiree's Baby," Desiree seems to have attained the life of her dreams. From her infancy as a foundling to marrying one of the wealthiest and most prominent plantation owners in the area, her life seems like a fairy tale come true. When she has her baby, she is as happy as can be, and Armand seems to become a gentler person. But when the child is about three months old, everything changes. Armand starts to avoid them.
As we find out through the progression of the story, as the baby grows, it becomes more apparent that he has African features. Armand infers that Desiree, whose parentage is unknown, has black ancestors, and because of his racial prejudice, he can no longer love her. When Chopin uses the words "her child" instead of saying "their child," she is describing the rejection that Desiree feels from Armand. He seems to not even acknowledge that the child is his. At this point in the story, Desiree is confused because she doesn't yet see the African features in her child and can't understand the change that has come over Armand.
Chopin is also using the literary technique of foreshadowing in which authors hint at something that is to come later in the story. Calling the baby "her child" subtly sets up what happens later when Armand rejects both Desiree and the baby.
The use of "her child" also hints at the strong patriarchal system Desiree lived under. There are hints in the story that Armand has fathered other children with his slaves, particularly La Blanche. In those cases, too, the child would be considered "her child," not his, although he should have played the role of father socially and morally, not just physically. The words bring out one of the themes of the story, that men wield absolute power in that society, and that women and children are on their own if the man refuses to acknowledge them as his.