Because Homer clearly opposes Emily's wish, he is considered an antagonist in this story.
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Emily is definitely the protagonist of the story, but she also serves as one of the story's antagonists. Emily is Homer's antagonist because she is his murderer. In addition, she serves as an antagonist to the community because of her hautiness and feeling of entitlement due to her family's former position in the town.
In contrast, the town also serves to antagonize Miss. Emily. The residents initially attempt to provide comfort and help to Miss. Emily through trying times. Unfortunately, they also have a part in Emily's situation with Homer. Their actions precipitate his death, and we can't leave it there because Homer would have to accept responsibility for his part in their failed affair too. Notably, he can't answer for his actions, and we aren't really apprised of them either.
Lastly, there's Emily's dad. His influence on her life, as well as his refusal to allow her any kind of individual happiness isolate her from outside influences. She's ignorant of the world around her and unable to assume any kind of adult responsibility because she's never been allowed to experience anything. Thus, Mr. Grierson can be typecast as an antagonist along with everyone else.
A Rose for Miss. Emily