You're angry, they're angry, now what? The highly respected Vietnamese Buddhist monk, Thich Nhat Hanh has some good words for this in his book Anger: Wisdom for Cooling the Flames
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His basic message is this:
When we are angry, it is very clear in that moment that we are suffering. But what is not that clear to us is that the other person's anger means that they are suffering as well. What we more often do is see them as the oppressor which makes our anger boil even more. Therefore it is really helpful to be able to understand that they are suffering in the moment to which lends us to behave more compassionately. This is often really helpful in not only stopping the escalation of anger, but also opens our hearts to feeling compassion which is an emotion that is connected to well-being.
Try: Think of a person who you are angry with or have difficulty with. If it is extreme anger, try and choose someone a little less triggering. Think about all the reasons you are angry with them. Think about what makes this person happy and what also makes this person suffer in their day to day life. Try and put yourself in their shoes and see what reason they have for being angry. Consider whether they are acting from a place of prejudice or narrow-mindedness. Consider whether the person is aware of or a master of their own thoughts and emotions or whether they often act from a place of auto-pilot. Consider again how they must be suffering. Do this until you feel compassion beginning to bud inside of you. Having compassion for someone does not mean you think what they are doing is right or skillful, but it releases the anger from you.