Well, when you're angry, you do burn yourself mentally. Everyone knows how anger feels like, right? It's not an enjoyable feeling.
Of course, you can inflict damage upon someone else with your anger (which is why it implied that you can "throw the hot coal at someone else"), but it will not always happen - and your anger may not always inflict damage, thus you're the one suffering most of the time (or maybe the entire time). The damage inflicted on a foreign being by one's anger is far weaker than the damage that the protagonist is mentally receiving from his anger.