I would wait for a true native speaker to jump in and explain, but as far as I've gathered, instrumental is generally used (at least formally so) in být + profession constructions. E.g. "Stala se lékařkou, když jí bylo 25", "She became a doctor when she was 25." The concept of "profession" here is a little more loose than might otherwise be expected. Thus student, neighbour, or parent all count as professions and when you are talking about becoming one or that you were one or that you are no longer one, you use instrumental.