Here's a concrete example. I hired somebody who was really impressive during the interview process, but then soon realized they just didn't have the right skills for the role. He wasn't a bad person. Had a family, and I knew it would be a big disruption for them to have to go through job searching again.
Another case. A guy I managed caused a lot of friction with one particular co-worker, and it came to a head when he he stepped way over the line and veered into personal attacks on a call. Had to let him go, and I was angry with him at the time, but it still pained me to do it and was on my mind for quite some time.
I agree those are two common scenarios where it would be painful. Those two people were not good fits for their roles, so hopefully they found something more appropriate.
Another case. A guy I managed caused a lot of friction with one particular co-worker, and it came to a head when he he stepped way over the line and veered into personal attacks on a call. Had to let him go, and I was angry with him at the time, but it still pained me to do it and was on my mind for quite some time.