Understanding or having an appreciation of a character's circumstances is a huge asset when discussing or analyzing character motivation. The most important aspect of the Misfit in Flannery O'Conner's "A Good Man is Hard to Find" is that he is a psychopath, a man bent on destruction, violence, and cruelty. O'Conner richly develops his total lack of remorse and hardened edge in his dialogue with the grandmother:
"I found out the crime don't matter. You can do one thing or you can do another, kill a man or take a tire off his car, because sooner or later you're going to forget what it was you done and just be punished for it."
His motivation for the killing the family is two-fold: (1) He kills them because he can, and it makes him feel powerful. (2) He is on the run from the law and does not wish to leave any witnesses behind to go to the police.