Here's why:
* Nourish, feed, and supply all relate to providing sustenance or resources. They can be used in the context of physical nourishment (food) or figurative nourishment (ideas, knowledge).
* Inculcate means to teach or impress something deeply into someone's mind. It implies a process of instilling beliefs, values, or habits.
Therefore, while the others focus on providing something, inculcate focuses on instilling something.