I think that privileged persons often don't look beyond their own nose (had to look up the expression. In German we say "über den Tellerrand schauen" which literally means "to look beyond the edge of a plate"). Even if their parents didn't go to university, they certainly have the money for a good or very good education. That's not the case for all students from a non-academic background. There are people who don't have the money to put their children in a private school or pay for extra tutors etc. or they don't encourage their children to do well in school. At my university there is even a student association for those from a poor(er) background, from non-academic backgrounds. The association is quite new. The majority of students still comes from a "better" background, but there is a shift and acknowledging this and helping those students is important.
But if the privileged students (both those with parents who went to uni and those who didn't but have enough money) don't see that, they really need to broaden their horizon.
I may be more privileged than others too because I could afford to start studying at 30. I know that others, who went to the same second-education-school as me, couldn't because they hadn't the money and I know that one person couldn't get student loan because you have to go straight to uni after leaving this second-education-school (it's a bit complicated). That means if you get your Abitur certificate in winter (at "normal" for schools for teenagers there is only one time, but at second education you can start and leave the school in winter or in summer), you have to apply at uni for the course in summer otherwise you don't get the loan (that only applies for 30+ year old students). Yeah, as you can see: the German education system is complicated.