Nonetheless I take issue with the idea of professors being employees of the students. This is not the case, staff in a University are only answerable only to the administration.
In the US, school staff would not be considered employees of the students because the students do not direct the staff's actions - a key component in the criteria that determines the existence of an employer/employee relationship.
University professors are employees of the university.
Students are clients of the university. As such, they have legal rights under consumer protection and relevant laws which regulate commerce. But they do not exercise the rights of employers.
Gotta be careful with metaphor and analogy when dealing with legal issues. The law may deal with legal fictions. But it doesn't indulge in metaphor or analogy. Weird as it may seem to most people, legal theory is a very precise and specific thing based on existing case law rulings and legal concepts which themselves tend to have precise and specific definitions.
And it's also important to remember that courts are "courts of law." They're not
debating societies or forums for public opinion.
In the US, that's the function of the legislature - not the judiciary.