Perhaps "argument" is going a bit far -- the ideas don't really cohere enough to qualify for that -- but you have to grant the outlier part.
Kevin Carey has just discovered that people who stack up normal debt getting a bachelor's, then take out more loans to go to law school and don't graduate, then take out more loans to go to grad school and don't graduate (and also use student loans for other things like child care), then get a life-threatening autoimmune disease, then get screwed in a divorce and then take a string of low paying jobs and make a number of really bad financial decisions can rack up quite a tab.
We should probably stop here for now. There is nothing instructive in the case of Carey's example, Liz Kelley. The only lesson one can reasonably draw here is that people with bad luck and incredibly bad judgement tend to fare poorly in life.
Joseph and I are planning to come back to the rest of Carey's hopelessly muddled reasoning later. That's not to say that everything he says is wrong (life is not a knight/knave puzzle). The system is horrible, just not necessarily for the reasons he gives. Subsidizing higher education through student loans creates all sorts of perverse incentives, it sends too much money to undeserving institutions and it allows a few people like Kelley to spend far too much taxpayer money. It isn't difficult to argue against this system, but if the NYT Upshot wants to maintain its reputation, the paper should probably find someone other than Carey to make the case.