I will quote the rest of that chapter in Romans 12: 20,21 as part of my answer. " No, if your enemy is hungry, feed him; if he is thirsty, give him drink; for by so doing you will heap burning coals upon his head." " Do not be overcome by evil, but overcome evil with good."
You can find out a whole lot about the reasons for peoples evil behavior by being nice to them. There are reasons behind people's evil actions. God knows the truth about all of us. He tells us to leave it to Him.
When we are nice to someone who is evil, it can change their whole life around. Think about it, have you ever been in a real foul mood and said or did something nasty to someone? Perhaps someone you didn't know witnessed it and judged you to be an evil person, but you are not really. Then they started telling others about your evil actions and they began to judge you on this too. Everyone thinks you are evil now, so perhaps you start to act more nasty, because, " Well, that's how everyone thinks I am anyway." Now think about this, if that person who didn't know you, had come over to you later and spoke kindly to you, perhaps you might have explained that you were having a bad moment and you really didn't mean it. Now things would be different. Now he would be telling others that you aren't such an evil person, it was just bad reaction to a bad day. You see if we take the time to be nicer to each other, we can over come evil. God made us, He understands us better than we understand ourselves. IMHO
