What would you call Coursera and Udacity then? Because they're both for-profit...
Non-profit institutions have a goal of education and/or research. For-profit education is designed to soak the uninformed, with the exception of education that is for person A, but purchased by person B. In that case, it is possible for person B to be an informed buyer.
Basically, the market for education is subject to many market failures. For-profits exploit these to the detriment of all.