In my view, it does not make sense for employers to be allowed to file grievances, at least if we are talking about grievances filed against workers or the union. This is because the employers have more power than the workers and do not need to file grievances.
Employees and union members need to be able to file grievances because employers can do things to them that are unjust. An employer, for example, could conceivably fine a worker for taking too many bathroom breaks during a shift. The employer has the ability to do this because the employer is the one who actually writes checks to the employee. The employee needs to be able to file a grievance to reverse the employer’s action.
In contrast, employees cannot really do much to harm employers. This means that employers do not need a grievance process to remedy harm done to them. For example, let us imagine that an employee does something that they are not allowed to do. Let us imagine that they decide not to come to work on a given day. The employer does not need to file a grievance in this case. They can simply fire the worker (assuming that is consistent with their policy). They have the power to punish the worker for violating his or her terms of employment.
Workers do not have the power to punish employers for violating contracts or other terms of employment. Therefore, they need the ability to file grievances. Employers have the power to punish employees for violations. Therefore, they do not need the ability to file grievances.