A person who thinks government-run schools are a model for colleges to emulate might be hard for you to convince along merely economic lines of argument.
You might, however, try a reductio ad absurdum. If it’s a good idea for the government to set the price of a college education at zero for students and then raise the funds to pay for the resources used to provide such education by taxing other people, then why not do the same thing for automobile production or tablet computers. If fact, if it’s such a great idea, then why not have the government provide everything for free by taxing everyone.
Links to several articles on public education can be found here: