Earlier quoted context omitted.
I read long ago: Firing someone is admitting to your second mistake. (Not being able to exploit the talents of someone you hired. The first mistake is hiring someone who you later have to fire.)
That's kind of a shitty saying. We all make mistakes but the way that's phrased makes it sound unforgivable. The ramifications of hiring are bigger than your everyday mistake but it still happens.
I guess it is bad if you are the manager who is responsible for both mistakes.
Otherwise, it is a reminder that it is a failure to hire someone that doesn't work out, and a failure to not be able to use someone as most people have some skills and firing someone is a very harsh thing to do both to the ex-employee in their ex co-workers.