So there can never be two sound-minded people holding real grudges against each other at any given time?
A deadly grudge between two people with totally sound minds is extremely unlikely. If someone wants to kill anyone, he's either a moron himself (like Chapman) or the person he wants to kill is one (a rapist, a murderer, a power-abuser).
Two soldiers fight on opposite sides. The father of one of them participated in a raid that killed the other's family (collateral damage; hey, it happens). The other captured the father and executed him for war crimes.
They both followed orders, and they both want to kill the other.