That's why I was really surprised about the content of the article (to be honest I haven't made it past the TL;DR yet), I would have guessed that the problem would be too little egalitarianism.
Kids here are sorted into career paths at age 10 by sending them to Gymnasium, Realschule, or Hauptschule. To even attend higher education you need to have an Abitur, which means going to a Gymnasium or putting in extra years of study after your Realschule.
The argument is that this division allows every kid to learn at a level appropriate to them, but the reality is that an overworked teacher of 20+ kids is supposed to accurately assess everyone's level and then give a recommendation for one of the schools.
My impression is that a lot more weight is put on formal qualifications here than in the US, so in practice this choice sorts you into your future social status for most kids.
My N=1 annecdote is a friend of mine who recently finished his PhD at TUM, the teacher wanted to send him to a Hauptschule. If his parents hadn't intervened his life would probably be very different right now. Annecdotaly I know a couple of engineers who went to Realschule and then had to work hard to get an Abitur before going to Uni. Who knows how many smart people were discouraged from pursuing higher education because it would mean two more years of high school just to even start.
The system seem arbitrary at best to me, and at its worst is just reinforcing class status through generations. Parents with university degrees will fight to have their kids go to Gymnasium, or the teacher might send them because they know they come from an Akademikerfamilie, and the others better hope their teacher likes them.