I don't think thats the case, within the families. My experience is that parents who don't have college degrees are much less likely to financially support and/or push for college for their children. The idea that the only way to make it in life is to graduate from college is a societal view.

Now you'd think that someone who didn't graduate college would see its value, but they're probably less likely to be able to help their kids financially (especially in the middle-area where the parents make too much for the kid to qualify to student aid, but not enough to comfortably afford it). Also cultural differences - conservatives are pretty unlikely to want their kids to go to a "liberalizing" college institution.

"First generation" college students also go to 2-year colleges at a far higher rate, and are far less likely to go to a private college than students who's parents completed college, and were also far more likely to drop out because of economic reasons. 33% drop out within 3 years vs 14% of those with parents who went to college.

https://www.insidehighered.com/news/2018/02/08/students-post...