Miss Emily, by the time she met Homer Barron, was already past the proper age for marrying in the culture of the old south. In fact, her relationship with this Yankee was looked down upon by the town and her family members who came to visit.
The reader already knows that Miss Emily is comfortable with corpses, because of her father, and the fact that she buys men's clothes and rat poison, in conjunction with Homer Barron never being seen again, lead to the conclusion that she poisoned him to keep him from leaving her again.
The town, as well as Miss Emily, came to understand that Homer Barron was:
"not a marrying man" (Faulkner)
The town believed that Miss Emily:
"would persuade him yet, because Homer himself had remarked--he liked men, and it was known that he drank with the younger men in the Elks' Club" (Faulkner)
The story suggests that Emily killed Homer Barron because she believed that he would not marry her and that she wanted to make sure that this gentleman caller did not get away.