A private university, especially privileging students from finance backgrounds, is about as far from communism as it gets.
In theory. In practice (history is full of it), the castes develop overnight. A group of individuals has to make decisions and manage the oversight and record keeping, etc. This leads to corruption and a de-facto aristocracy.
Is that not privilege? Why could a government official get a car while a normal person would have to wait years?
Children of government officials got preference at the best universities and jobs. Is that not aristocracy?
Communism is all about privilege — everyone is equal but some people are more equal than others.