Non-profit, mostly, have standards for admission. The for-profits don't. They just want people to spend money. Faculty at for profit colleges get fired if their standards are too high. The for profit system is all about getting students in and making sure they never fail a course. Keep them paying. For profit motive in education as it currently exists is a disaster.
For profit education is great for giving a single individual specific skills they need that will make them money.
For profit education is unlikely to be interested in giving a person a "wide liberal arts background". And the thing about a wide background is that isn't worth much to the individual in terms of money. They might look back on their lives as having been richer for it or they might not. But giving a person a wider background is worth more to society as a whole, in everything from life being more interesting to politics being less polarized.
There's an assumption here that for-profit ventures perform worse or serve interests worse than non-profits. In my experience with non-profits, there's lower accountability, higher salaries with less performance, less accomplishing of the organization's objectives, and more corruption and politics. Nonprofits have historically done very poorly at their stated aims, and vastly, vastly underperformed for-profit companies in building up the world. Also, the majority of universities and schools are already set up as non-profits, which might be part of why they're so dysfunctional.