The major explanation I've heard is neither of those (though its a more general version of the Bowen explanation), but simple market-specific demand-pull inflation: higher education has increasingly become perceived as essential, so more people want to buy it and those who would have been willing to buy it anyway are less price sensitive, so the market-clearing price goes up.

(This is different than "eating up subsidies", since, while the subsidies are a contributor, they aren't generally viewed as the only, or even the most important, driver of increased demand.)