Not really in users directly, as there is no such relation as "User owning users".
Roles is the way to go if the groups not change too much, but you are going to need to define a different role to group students for every teacher, and properly getting out of that role students no more assigned to that teacher.
It could be more easier to maintain two roles, teachers and students, and with user_meta validate if the student is currently overseen by the teacher and therefore is able to handle student's posts.
The specifics are very difficult to write down here unless you have already defined how do you want to proceed. The plugin recommended in the first comment requires no code but maintenance by hand of roles for every user.