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"

English uses "of" to replace a number of Greek and Latin genitives. So in this case it is a "genitive of source." School is the source from which the student dropped out. That is a very technical answer, but the phrase is a set one, so you can just accept it as it is and use it, if you like.