In a 1959 interview, William Faulkner explained why he titled the short story "A Rose for Emily"--in essence, he said that she had experienced so many disappointments in her early life that she deserved something as beautiful as a rose:
. . . it's simply that she had no life at all. Her father had more or less kept her locked up. . . . In this case there was the young girl with a young girl's normal aspirations . . . who was brow-beaten and kept down by her father, a selfish man. . . .
Even though Miss Emily ultimately murdered her "suitor," Homer Barron, Faulkner had a difficult time imposing a harsh moral judgment on her actions because he felt that those actions were, in part, a direct result of her relationship with her over-bearing and selfish father.
All we know of Miss Emily's father is that, when she was a young woman of marriagable age, "none of the young men were quite good enough for Miss Emily and such," the implication being that Miss Emily's father, not Emily, rejected all possible suitors. Emily's father, then, cut off Emily's hopes, as Faulkner put it, "to find love and then a husband and a family." Once the group of eligible suitors was eliminated, Emily's chance for a normal life disappeared.
If there is any doubt as to what kind of man Emily's father was, or what their relationship was like, the town tells us
We had long thought of them as a tableau, Miss Emily a slender figure in white in the background, and her father a straddled silhouette in the foreground, his back to her clutching a horsewhip, the two of them framed by the flung-back front door.
We are presented with a symbolic representation of a dysfunctional relationship and a cruel man. The fact that Miss Emily stands behind her father, with her father "a straddled figure" in front, indicates Miss Emily's subservient relationship, and the whip in her father's hand can only represent his controlling and cruel nature.
Although it is a cliche to say that Miss Emily represents a repressed woman, it is nonetheless an accurate statement of her condition. That the repression came from her own father is especially cruel--a man who should have had the interests of his daughter in his heart turned his back to her figuratively and literally, thereby setting in motion the events of Miss Emily's blighted life and her attempts to achieve her version of a "normal" life.