Privatize, yes, but why for-profit?

I'm all for competition between schools - the number of colleges which sent me crap because I happened to do really well on the PSAT made it so that I realized I could go off to college a year early - but for some reason the idea of schools competing for students is usually followed by making them for-profit. I don't see why - Schools are more about doing something nice for the kids than making money off of them, and I think the fact that even colleges which have completely eschewed government interference (such as Hillsdale College) demonstrates that it doesn't make sense for schools to be for-profit. Teachign will never be a lucrative profession - it's like venture capital without the payout - and making schools for-profit will just make education less available, which isn't the point.