Jobs and schools, any organization hires "at will" meaning they get to decide how to run their business. I think, since your school gave you a choice of secondary exercises to to do to show you want and have what to takes to be a teacher, I would do that if that's what you want, or not.

You cannot just quit a job for illness; they need someone to do that job and if you are not able for any reason to do it, then that cannot be the job for you. It is unfortunate that you are/were ill but that cannot be their problem; they have a business to run.