When Miss Emily tells her visitors that her father is not dead, she is doing several things. First, she is denying reality. She does this in different ways throughout the story.
A related point is that she denies her father's death because he played such a large role in her life and identity. It is almost as if she cannot accept that he is gone, or can't conceive of herself without her father.
Also related is the fact that with the death of her father, Miss Emily's status in the community changes. The longer he is alive, or that she can claim he is alive, the better her status.
A final reason is more subtle and pervasive. Emily's position in her community allows her to control the reality around her. Denying her father is dead is parallel with denying she owes taxes.