The first time I fired someone, I was completely crushed. But I was lucky to have that go particularly well in the long run. It was clear to me why this person wasn't going to succeed with us. I offered to give advice during their ensuing job search and they took me up on it. They had two offers at two very different companies. It was clear to me that they would have the same trouble at one but would fit the other. They had the same sense and they immediately found more success than they'd ever had before. A year later they reached out to tell me that firing them showed more care than any manager / mentor / teacher had ever shown them and it helped them take the next big step in their career.
It's still not easy for me to say things that I think might make people uncomfortable. But the experience of firing that person is a constant reminder that speaking hard truths is the deepest kind of caring a manager can show.