Human nature doesn't want to hurt others. So anger can't be part of human nature, since anger wants to hurt people. Let me also use Plato's argument here — why not borrow from others when they support our point? Plato says: "A good person doesn't hurt anyone. Only punishment hurts people. So punishment doesn't fit with being a good person. And since punishment and anger go together, anger doesn't fit either. If a good person takes no pleasure in punishment, then he won't enjoy the feeling that makes punishment pleasurable. Therefore, anger isn't natural to humans."
Man’s nature is not, therefore, desirous of inflicting punishment; neither, therefore, is anger in accordance with man’s nature, because that is desirous of inflicting punishment. I will also adduce Plato’s argument—for what harm is there in using other men’s arguments, so far as they are on our side? “A good man,” says he, “does not do any hurt: it is only punishment which hurts. Punishment, therefore, does not accord with a good man: wherefore anger does not do so either, because punishment and anger accord one with another. If a good man takes no pleasure in punishment, he will also take no pleasure in that state of mind to which punishment gives pleasure: consequently anger is not natural to man.”