I don’t think firing someone should feel good. However, you need to get over it and recognize that the firing is required for your health, the health of your business and your other employees. Trust me when I say you would feel much worse if you allows a bad person to stay and it destroyed those other things. Suck it up, you don’t have the bandwidth to feel so bad.
I think this is fairly normal. You’ll grow into new circles with friends who don’t feel that way. It’s ok.