Of course not, but a manager's job is to "manage" a business without making it personal.. If an employee isn't performing their work to the manager's satisfaction, then it's the manager's duty to cut them.
Peter......I suppose this would have to do with any given company, institution or business and their respective policies and authority delegations. However, having been in middle and upper "management" through most of my employment history, I not only had the authority you mention, but this was an integral responsibility.
Management by it's very nature is more often than not expected to interview, screen, hire, train and supervise first line of staff. This being a fact, there are always a list of rules within a company as well as State Employment rules & regulations, often Unions, which protect employees from unfair practice. Should someone feel they were unfairly fired, there are numerous options that employees have to file grievances and appeals.
It sounds as though you have experienced a personal situation. If this is the case, I would strongly recommend that you look into any options that may be available to you at your place of employment.
I see that you do not live in the U.S.A.....so I'm afraid I have no knowledge of just how these business practices play out in Countries other than my own.
I hope I have been of at least some help to you. Peace, Paula.