What makes "A Rose for Emily" a gothic or Southern gothic story?
The American Gothic movement sprang from the Romantic movement. The Romantic writers focused on individuals, trusting yourself, and believed that mankind was noble and ideal. It contained elements of the supernatural, had really good heroes and really evil villians, and forged the path into the individual being the focus of many stories. From this, the Gothics took a turn for the dark. They too had supernatural events, focused on the individual, and had really cool villians, but, instead of focusing on what was good and ideal in mankind, they focused on the darker side of human nature. The American Gothic movement was like the evil twin of Romanticism; it delved into insanity, crime, evil, and the dark side that each human being has buried somewhere in their souls. So, those characteristics defined the Gothic movement here in the states.
"A Rose for Emily" contains a character who definitely caves to her darker side. It tells a story of a woman who is willing to kill someone that she loves so that they won't abandon her, but, beyond this, lives in a delusional world that allows that person to still be real to her, real enough to sleep next to on a bed and pretend to cuddle. This storyline exposes the darker side of Emily's nature, reveals the "skeletons in her closet" (literally and figuratively) and makes the point that even the social elite of the old South are subject to the horrors of evil and the downfall of insecurity and immorality. It also presents a good mystery to puzzle out, and is set in a decrepit, old, decaying house and town; other elements of gothic fiction.
I hope that those thoughts help a bit; good luck!
This story embodies some other characteristics of Gothic literature, in addition to those already discussed by others. First, Miss Emily's home strikes the reader as an especially Gothic sort of structure because of the secrecy and mystery that shrouds it. Miss Emily's father died there, and later, after Homer Barron's disappearance, only her servant comes and goes, and no one else is allowed in. Then there's the strange and awful smell that begins to emanate from the home. It's all very mysterious and dramatic, and this kind of setting is very common for Gothic literature.
Miss Emily herself is also shrouded in mystery, especially as a result of her self-imposed isolation. She is isolated even as a young woman as a result of her father's belief that no one is really good enough for her. Suitors are turned away until they stop coming. Then her father dies and she refuses to let officials take and bury the body; it's very odd and makes it seem as though she is not quite in her right mind. Then Homer Barron disappears, and everyone assumes that he's left her, making her sort of sympathetic but also even more strange. Then, her isolation later in life, which seems to be her choice, increases her strangeness and aura of mystery. The dark mystery surrounding Miss Emily herself, as well as her home, is very Gothic.
"A Rose for Emily" illustrates several Southern Gothic traditions. The setting of Emily's old Southern home reminiscent of the antebellum South is a key element of Southern Gothic literature just as the mysterious castle is for traditional Gothic works. The house remains closed off to outsiders throughout most of the story, adding to its peculiarity.
Emily, like many Edgar Allan Poe characters, is eccentric, intimidating, and misunderstood. In addition to closing her house off from society, she also shuts herself away from the world. Also like Poe's Gothic characters, she has endured pain and loss at the hands of others and exacts revenge upon her "tormentor"--Homer Barron.
Faulkner's description of the interior of the Grierson house lends the story best to the Gothic genre. When the town leaders visit Miss Emily about taxes, Miss Emily's servant opens the long-closed blinds, and "a faint dust [rises] sluggishly about their thighs spinning with slow motes in the single sun-ray." Emily and the house are accustomed to a lack of use. Likewise, Faulkner's macabre description at the story's end of Emily's bedroom where Homer has been entombed for years surprises and shocks the reader. Poe and Hawthorne often followed this pattern for their Gothic tales.