The Greeks thought that a hero needed to have courage, boldness and quick thinking.  Perseus had the courage and boldness to confront the king, cut off Medusa's head, and turn the sea creature to stone.  His quick thinking helped him to snatch the eye and tooth from the gray sister's hand, and pull the Medusa's head from the sack in order to turn the sea monster into stone. The Greeks admired these qualities because they help you fight against the problems that appear, and help with emotional doubts and mistakes.