This is not correct. It depends on the Bundesland (state) you live in. Some have mandatory assignments to a type of secondary schools, in others it’s up to the parents.

That said, switching from one type to another during secondary education is far from impossible, but also not always easy and smooth - it depends a lot on the school you leave and the school you enter. On the other hand, it’s very easy to start an academic education when you have finished your vocational training. More than one third of college students don’t have the „Abitur“ (graduated from Gymnasium)