In Germany, if a young person isn’t up to the standards of the gymnasium (grammar school), they may progress into a hauptschule – for the non-German speakers, "general school" – which helps learners move towards vocational education. So instead of a Year 6 pupil following their friends into gymnasium, they would venture elsewhere.
He hasn't quite done his homework on this. Many German schools are moving away from holding children back, although some primary schools have introduced a system in which children can complete the first two years of primary education in either one, two or three years, by using mixed-age classes.
They also don't just have the choice between "Gymnasium" and "Hauptschule" (I think in Bavaria they might, but they are a slightly special state all by themselves). Those, wo don't make it into grammar school (after Year 4, based on teacher assessment/parental preference depending on the state) generally move to a "Realschule" or "Mittelschule". Most parents don't want their children to go to a Hauptschule...in many states, that's one tiny step up from being sent to special school, which is why they are being disbanded.
It's also possible to switch between schools and streams during secondary and a lot of it is based on parental choice. Not many children go to independent schools...unless they've got 'issues'. 