The preposition 'of' means being part of something/relating to something
In your example the student is considered a part of the school...until they drop out. The school is not just the building. It is the group of people (students, teachers, administration staff, etc) that constitute the organisation.
Also, though you often see 'to drop out' as a phrasal verb in dictionaries, in fact I'd say it's worth thinking of it as a three word phrase and learning it this way. Even sentences like "He decided to drop out" omit "...of university/school/the course/the team/etc"