The individual reader has to decide for himself about the amount of sympathy that is due Miss Emily. Her decision to apparently poison Homer Barron rather than allow him to leave her was a simple act of murder. However, many readers find her a highly sympathetic character who acted out of a desire to retain the man she loved. Her past relationships with men (especially her father) probably led her to make such a gruesome decison. Her mental instability has to come into question, and for this reason many readers may excuse her for her actions. She is a character to be pitied, but not necessarily forgiven for her transgressions.
There is no "argument" in Faulkner's "A Rose for Emily." It is a fictional short story, not a nonfictional essay. Argumentative essays present arguments, the best fiction usually doesn't, especially in the 20th century.
Faulkner, of all writers, knows better than to present fiction that provides easy one-liners that presume to tell people how to live. His fiction is filled with ambiguities, as is life. There is no "message" argued in the story, only ideas that are raised and situations that are treated. Faulkner's story is above giving simplistic answers to its readers.
The desperation of the South following the Civil War is treated. The loss of the South's economy is presented. The reluctance to change and inability to adjust are featured. As is mental illness.
Issues of parenting are touched upon, and issues of isolation and of alienation are present as well.
Faulkner depicts human existence; particularly human existence in the South following the Civil War. He doesn't preach or teach or pretend to have nice, neat, easy answers to life's difficult questions. He knows better.
There are several messages sent in the story, particularly that of the struggle between the past and the present, and the inability to let go.
In Emily's case, she went from an Aristocratic Southern family to a lonely, and archaic existence in a place which time has changed.
Her stubborness in paying taxes, her attachment to her father, her need for Homer, and her eventual retaining of his corpse after killing him clearly demonstrate the argument that, to some people, change and progress are actually threats to their lives, as they know them.