One of the key themes of this excellent story by William Faulkner is the way in which blood or lineage is so important and can lead to a sense of social superiority. It is clear that Emily Grierson represents an old, passing order of time, and she feels that she is worthy of respect and special treatment because of her social standing. The text tells us it is this sense of social superiority that leads her father to keep her single, and it is this act that makes people begin to feel sorry for her:
That was when people had begun to feel really sorry for her. People in our town, remembering how old lady Wyatt, her great-aunt, had gone completely crazy at last, believed that hte Griersons held themselves a little too high for what they really were. None of the young men were quite good enough for Miss Emily and such.
Note the reference to superiority and that Miss Emily was regarded as "too good" for the young men of her society. We are then given the rather disturbing image of the father with the horsewhip, preventing any suitors from seeing her daughter.
Additionally, the level of control that Miss Emily's father exhibits points to a man who is afraid of letting go of his daughter. She is all that he has, and he is unwilling to part with her. No matter how good the suitor might have been, he was not going to allow anyone to take her away from him. This is important thematically because it helps to explain, to an extent, why Miss Emily, in turn, seeks to exhibit the level of control that she does over Homer Baron. Her father would not let her go, and she is not going to let Homer go no matter what. Even if she has to kill him (which it appears that she does), she is not going to allow him to leave and potentially find someone "better" - similarly, her father may have exhibited that same concern - that Emily would marry and discover a man that she felt more affection for than she did for her father. This is a great example of co-dependant behavior!