One reigning theme in "Fur" is friendship vs. convenience, among many other themes that could be extrapolated from the tale.
In this story, two women who are friends, Eleanor and Suzanne, are plotting a way to let Suzanne's rich cousin know that she wants an expensive fur for her birthday. While they are about to carry out their plan, Eleanor asks Suzanne if she could do a favor for her as well: to sit in her place at a game of bridge, hosted by some "boring" aunts, in order for Eleanor to see her beau.
Suzanne is a woman who is described as someone who thinks that
the sacrifices of friendship were beautiful in her eyes as long as she was not asked to make them.
Therefore, she refuses to do the favor for Eleanor even though the latter is currently doing a favor for her. This type of "friendship for convenience" and the poor balance of sacrifices that each woman is willing to do for one another are the central topics that the story reflects. Still, there is one more theme, which is revenge.
When Eleanor sees Suzanne's refusal, she actively and discreetly switches her goal and ends up convincing the rich cousin to buy her (Eleanor) a fur after she "revealed" to him the sad story that her family cannot buy her nice things. Not only did she manage to snag the fur for herself, but she also suggested the wrong present for Suzanne's birthday, which was a fan; something that Suzanne absolutely does not need.