In 1959, Faulkner gave an interview in which he answered the question why he titled the story, "A Rose for Miss Emily."
Essentially, Faulkner said that the story was about a woman who had "no life at all." Her father, the real villain of the story, had prevented Emily from having a normal life--he sent away every eligible suitor she had when she was of marriageable age because they were, from the father's viewpoint, unsuitable. So, her life centered on the care of her father, and she was deprived of a normal upper-class woman's life--finding love, getting married, having children and a home. Instead, she spent her productive years taking care of an intensely selfish father who "wanted a housekeeper." Faulkner then said the natural instinct for domestic life, if it is repressed, comes out "very likely in a tragic form," in Miss Emily's case, as a completely perverted attempt to replicate the normal life that she couldn't have.
In the end, according to Faulkner, even though she was a murderess, she deserved such a simple thing as a beautiful rose to make up for the life she was never allowed to have.