The gender conflict in this story is based around Katrina Van Tassel wanting to do everything she can to keep both of her suitors hanging on without discouraging either of them. It is significant that it is this strategy of hers that brings Ichabod Crane and Brom Bones into conflict with each other, as both vie for her attentions and Brom, because Ichabod refuses to fight him, is forced to resort to playing a series of practical jokes on Ichabod with hilarious consequences. Katrina seems to be portrayed as a female who is cast in the mould of a "hard to get" beautiful woman, and this is something that causes conflict with both of her suitors, and indeed with the storyteller himself, the narrator who regales the reader with this tale. Note what he says about courtship:
I profess not to know how women's hearts are wooed and won. To me they have always been matters of riddle and admiration.
Women therefore are portrayed in this short story as enigmatic mysteries who are not able to be understood by their male counterparts, and both Brom and Ichabod fall foul of trying to understand the mystery of Katrina Von Tassel and woo her successfully. This, as the narrator goes on to establish, would be no mean feat, because to woo a "coquette" successfully is definitely a real challenge:
He who wins a thousand common hearts is therefore entitled to some renown; but he who keeps undisputed sway over the heart of a coquette is indeed a hero.
Gender conflict in this short story therefore lies in the attemps of the male characters to engage the affections of a female who is something of a "coquette" and who is determined to ensure that neither of her suitors is discouraged. The view of women as being mysterious and "hard to get" is one that is obviously shared by the narrator, who, in his own words, find them impossible to understand.