Here's why:
* Their relationship was mostly focused on romance: Ichabod was smitten with Katrina van Tassel, the beautiful and wealthy daughter of a wealthy farmer. He was more interested in winning her affections than in teaching her anything.
* Katrina was already well-educated: Katrina was from a well-off family and likely received a good education. Ichabod, being a schoolmaster, was certainly educated himself, but it's unlikely that he would have taught her anything new.
* The story focuses on Ichabod's pursuit of Katrina and the Headless Horseman: The story is more about Ichabod's fear of the Headless Horseman and the spooky atmosphere of Sleepy Hollow than about any intellectual pursuits.
It's possible that Ichabod might have shared some stories or anecdotes with Katrina, or perhaps even taught her a song or two. However, the main focus of their interactions was on romance and the events that ultimately lead to Ichabod's disappearance.