At the heart of the mystery surrounding Emily Grierson is her relationship with her possessive father, whose presence Emily never quite escapes (his crayon portrait hangs over her coffin at her funeral). The narrator describes Emily as "a slender figure in white in the background, her father a spraddled silhouette in the foreground, his back to her and clutching a horsewhip." We learn that "none of the young men were quite good enough for Miss Emily..." Thus, her father had "driven away" and "robbed her" of chances to be married and to leave his home.
It is not until after her father's death that Emily's mental instability is evident to the narrator, who reports three days passed and Emily had not acknowledged her father's death. He had to be "buried...quickly." It is a "long time" before Emily makes a public appearance again. Homer Barron and Miss Emily are seen "driving in the yellow wheeled buggy and the matched team of bays from the livery stable." Because Barron is a Yankee and a common laborer, the town considers him to be beneath Emily's social status. To the townspeople, Emily's lapse in noblesse oblige is further evidence of her psychological deterioration. Homer's disappearance, however, is not immediately connected to the arsenic Emily buys; it is attributed to her father's "virulent[...] quality [...] which had thwarted her woman's life..."
After her father's death, Emily entered into a relationship with Homer Barron, a "Yankee" that was foreman of a crew doing paving in the town. Their relationship was very controversial because of several reasons: he was a "Yankee" and she was a Southern "lady," he was "blue-collar" and she was a "blue-blood," and it was well known he preferred the company of men. Emily was unable to have suitors when her father was alive, so I'm sure she was thrilled to have a man to "court" her. Because she had not been allowed to have suitors and because she had difficulty letting go, she decided that she simply couldn't lose another person in her life that she cared about, so she murdered Homer.