I'm repeating some of the points in the article in my screed here, but, I think the key issue from my perspective (I graduated from a top private university in 2008) is that if people of my generation had jobs in line with our level of education this wouldn't be as big of a problem - as the example included in the excerpt illustrates.
In past decades, with my geology BS (and an MS too) with my specific interests and expertise I'd have been recruited right out of school to an oil company or similar where I would be making a lot of money even in entry-level positions (though actually I want to stay in academia, for the record) - according to professors and others who have been around for a while.
My friends with their other science and engineering degrees would be in similar positions. Indeed though one or two are actually in that position, it's not that bad for everyone... except they are now engineers at defense contractors, which is not something I'd do personally...
Instead we've had to beg and grovel to get anything, with only the luckiest getting jobs actually related to their education (or any job at all) - not to suggest that a job directly related to your education is something that's ever been super common... except that it is within STEM fields - and if they do it's at a salary far below what it's worth. And so those with loans find it difficult or impossible to pay them off.
Honestly I can scarcely imagine how bad it is for most people, considering how bad it has been for all the STEM people I know.
Actually... the other thing I glean from the article is that if we were able to get decent jobs, the situation would only get worse because they'd use that as a justification for increasing costs etc.