The basic problem according to Buddhism, is that emotions like anger and hatred are based on projections and exaggeration, not on objectivity or wisdom, and thus basically incorrect.
There is little need to explain what anger and hatred do to ourselves by means of the laws of karma; the misery we cause others will come back at ourselves. Nobody wants suffering, so next is a summary of methods which can not only reduce but even eliminate anger and hatred from our minds.
It must be emphasise that to completely eliminate these negative emotions from our mind is a lengthy psychological process, requiring study, mindfulness, reflection and honest observation of one's own mind. To begin with, meditation is an ideal method to review a situation in which one became angry. This has the advantage that one is not exposed to the actual situation, but one can review it much more objectively. When regular meditation gives some insight into what anger is and what happens to oneself when feeling angry, then one can gradually try to apply it in real-life situations, preferably of course before one is already under complete control of anger. It is a slow process, but the change in your life and the ones around you can profoundly change for the better.
"To be angry is to let others' mistakes punish yourself.
To forgive others is to be good to yourself."
"Hatred does not cease through hatred but through love alone they cease."