In the Witch World, there are two types of mentor-student relationships. One is the typical academy teacher and student, where people are more like passersby in each other's lives and might not contact for eight hundred years after graduation. The other is the more traditional master-disciple bond, as revered as parents.
Spider Teacher and Dorothy share that second type of relationship. They become united in interests after the apprenticeship, almost like family. The homebody witch must fulfill filial duties to Spider Teacher, while Spider Teacher's academic achievements will be inherited and voiced by the homebody witch.
To put it somewhat harshly, if Spider Teacher suddenly kicks the bucket, Dorothy holds inheritance rights to her teacher's estate, and she even possesses the primary right to inherit, ranking above Spider Teacher's parents, partners, or children.