If you want a form with a selectable list (which hence is public) then those options will be of course public in the profile. And more, since one can select the list where to subscriber, nothing blocks a student to subscribe to the teacher list.
I suggest, if the teacher are not in a great number, to add them manually importing them in a private list.
More, since you let people to freely subscriber to a newsletter selecting if student or parent, there is no problem to let a subscriber to select both the options (even if he’s a student which select even “parents” or vice versa).
Stefano.