She means that the men in Emily's life cause her to be trapped in a role of an aristocratic spinster, forcing her to live a sad, lonely life. Her father, the Southern beliefs of a woman's place in society, and Homer Barron transform Emily from a lovely, slender woman into a gothic character at her death.
Her repressive father drove away all of her suitors, leaving her nothing at thirty but the lonely house in which they lived. Emily couldn't bear the thought of her loneliness, and it took three days for them to get her father's body out of the house to bury it.
She's seen as "a tradition, a duty" of the town, "a sort of hereditary obligation." Emily lives in the past because the town's attitude toward her encourages her to. They don't make her pay taxes, and Judge Stevens, not wanting to "accuse a lady to her face" of smelling badly, refuses to let anyone talk to her about the smell of her house. Homer isn't a proper match for a Southern lady, and Emily, a "real lady," shouldn't forget her social duty.
Homer, "not a marrying man," leaves for three days and then returns. The town, expecting them to marry, is relieved that Emily will not be a "disgrace" and a "bad example". She couldn't have stood the public humiliation, isolation and loneliness if he left forever.
The rose is partially a symbol of the ideal of a pure Southern woman who keeps her own personal rose preserved forever.
The “Miss” that the town gives to Emily’s name indicates the “respect’ men gave women in the traditional south, which tends to put hem on a pedestal, suggesting they are more delicate, pure, and good than men. Faulkner’s story, however, demonstrates how this homage to women arises from patriarchal power, symbolized by the picture of Emily with her tyrannical father. As an adult, Emily uses this “respect” to her advantage by refusing to pay her taxes, with the alderman too embarrassed to press the subject as a result of her haughty demeanor, which comes along with the “Miss” designation. Later we see the townsmen creep around her house, afraid to confront her about the stink that we eventually understand is a result of the dead Homer in her bed. We finally understand at the end of the story, that while Emily might use the “miss” to her advantage, it also ties her to a romantic view of the past, which, as seen in her relationship with Homer, is her ultimate demise. In taking away the “miss” from Emily in the title of the story, Faulker frees her from the past, celebrating that freedom with a rose—hence the title, “A Rose for Emily.”