Is it legal to fire a coach due to the complaining of parents?
What type of coach? (public school, private school, or other?)
Do you have a contract or belong to union?
If you work for a private institution and do not have a contract or belong to a union, you can be fired if the parents complained about the way you coached or the way you handled their children. However, if you belong to an institution, you may still be able to appeal to the board or some other higher authority when the organization.
Public employees are provided greater protections. You should review the employee handbook to determine your due process rights.
Licensed and Practicing in New York