I was once offered a job as a supervisor that came in low. I made a counter to the offer, stating that I thought I was an experienced supervisor. I was told that based on my interview I was not an experienced supervisor; specifically, that I did not have enough experience firing people...
As a military leader, firing people was never an option. I had to make do with whatever troops I had. Sure, if soldiers failed to meet minimum requirements, they would be chaptered out and discharged. But if I let my soldiers fail to meet minimum requirements then perhaps I should be chaptered out as well. In the civilian world, I have been lucky enough to work in positions and for bosses that shared a similar view; firing people was an absolute last resort and would reflect poorly on me as a leader. It is the job of a leader to make sure that people never reach that point.
In every supervisory role, I have had high and low performers. But I have found that all people operate somewhere on a curve, and it is the leader's job to help them reach their maximum potential. A good leader can make a low performer meet minimum standards, a medium performer excel, and a great performer really take off. A poor leader will allow a low performer to fail, let medium performers sink to low, and will discourage great performers (whose performance can then fall anywhere on the chart). A leader should be, first and foremost, an enabler of others.
When dealing with low performers, the way ahead is the same each and every time. The low performer must be given every opportunity to succeed. That means checking up to make sure the subordinate has all the required training. It means that I must make sure the objectives and expectations are clearly explained. It means that I, as a leader, can leave nothing undone that may help the subordinate do their job correctly. I cannot even consider any disciplinary action (including, at some point, firing) until I demonstrate that the failure is solely on the subordinate. This requires patience and work.
How many times has a leader gone to a boss with a complaint about a subordinate and have the boss ask; "Have you spoken with them? Retrained them? Put them with another person to work with?" Firing people without putting in the effort to help the subordinate is a lazy way to manage. A leader that is not invested in their team's success and improvement will fail to help other members of the team improve, resulting in mediocre overall performance.
Theoretically, the world's best leader will always be able to find a way to motivate and enable anyone to be successful. Realistically, there will be people that should not be in a position. But I have found that circumstance so rare that I have yet to encounter it (in my vast, vast experience...).
To ask someone to come in as a leader with the understanding that they will be firing people is strange. As a leader, I would expect to be given the time to work with a team before I make any judgment calls about individual performance.
To continue the interview... I stated that I did not think experience firing people was a sign of a good supervisor. In fact, a supervisor that is experienced at firing people is probably not a very good supervisor. At that point I think both myself and the company decided that I was not a good fit for that position.