The best way to destroy an enemy is to make him a friend.

Beating someone leaves them standing there, still opposed to you and now with a fresh reason. The other route removes the opposition itself rather than the person, which is why it tends to hold. It also costs more, because curiosity toward somebody who has wronged you is harder work than contempt.

Pick one person you have quietly written off and try, once, to find out what they actually want. You are not obliged to like them or to forgive anything. Notice whether the animosity survives knowing more.