: Your analysis of the university system as capitalistic is incorrect. You first need to differentiate between a private university and a public one. A public university recieves huge subsidies from the government and its profits are reinvested into the campus.
SDF: Universities are still selling a product for a profit, this makes them capitalistic. The fact of the matter is that young people are still told that they will be more likely to get a well-paying job if they have a bachelor's degree, whether this degree is "marketable" or not, and that they will enjoy life more and make more "connections" if they go to college. Parents buy into this logic heavily.
The fact that "nobody forces young people to attend college" ignores the fact that almost everyone is forced to participate in capitalism. I wish I had the right to choose otherwise.
BTW, the agriculture industries receive huge subsidies from the government, this makes corporations like Archer Daniels Midland no less capitalist.
: A private university recieves no government money
SDF: I beg to differ. Private universities receive enormous government subsidies, most importantly from the loans the government gives to students attending these places. If these loans were to be withdrawn, most of these private universities would soon declare bankruptcy. The only university I know of that doesn't receive such subsidies is that bastion of ultra-libertarianism, Hilldale College.
: and is generally smaller. Private universities often grant very large scholarships to promising young students, often at a loss. The reason they do this is that they know that if that promising student becomes successful they will donate back to the university.
SDF: Thus it isn't a "loss" when private universities collect from their alumni and divert part of the money to scholarships. Using the above logic, we might as well argue that a business buys its raw materials "at a loss" and makes the money back when customers "donate" money for its goods.