Why can’t l switch from private to public health insurance as a student?

The private insurances are Dr. Walter or Mawista. I was told that if I get any of those I can't switch to public during my studies.

I already applied for TK and it’ll start at the same as my studies in October. My question is if I’m using Dr. Walter right now and have it end 21 days after my studies start (they only work with full months). Will my TK insurance get canceled? Who controls this?

I don't really understand this rule and who controls it. I also can’t find more information about this. Everything that I find is saying the same thing: that I can’t switch from private to public.