Deep down, Frank Castle wants to be a noble iconic hero like Captain America. He truly believes that what he is doing is wrong and that he wasn’t the killing machine he’s turned himself into. But, he also believes that he has no choice after seeing his family senselessly killed in front of him. At heart, he’s a good man and a soldier in conflict with himself. That’s the real appeal of the Punisher.
Actually Frank Castle doesn’t think what he’s doing is wrong, he is waging a one man war on crime. In the story by Garth Ennis “Return of Ma Gnucci” the Elite states that he will use all of the Punisher’s personal demons to torment him in the ways the Punisher killing his father torments the Elite, but Frank responds with “What makes you think I have trouble sleeping? I send my demons back to hell and I sleep just fine.” Frank the proceeds to shoot the Elite in the head execution style. The reason the Punisher is cool is because he crosses that line that no one else will. Frank won’t fight Captain America because he respects him as a soldier.