Of course, very few parents didn't want their kids to go into higher education of some kind, and I think for about 99% of parents with college education, their children going to college was already a forgone conclusion for them.
I wouldn't put the blame entirely on the parents or the kids though- practically every school I've seen advertises job placement numbers; don't forget about the lawsuits over law schools artificially inflating their numbers to get more students. If you're a parent seeing that, why wouldn't you push your kid into college?