I was able to feel in peace even though the situation, while he let that unrest him and feel anger.
The Brahmavihara Sutta (see also Wikipedia) mentions 'sublime attitudes' including equanimity and compassion.
To the extent that you develop equanimity, to that extent perhaps you can be content. If arrogance arises, so that you are no longer in a state of equanimity (no longer "devoid of ill will, unbewildered, alert, mindful" and "with detachment"), then there's little to be proud about any more! So perhaps it's self-limiting, i.e. when you're arrogant then there's nothing to be arrogant about.
Another thing is that the experiencing of anger is unsatisfactory. If you can skillfully avoid the experience of anger then you should probably feel Muditā i.e. "the wholesome attitude of rejoicing in the happiness and virtues of all sentient beings" towards yourself, i.e. "it's fortunate that this person didn't suffer from anger".
Similarly if another person is suffering because they're angry then compassion, "the wish for all sentient beings to be free from suffering", i.e. "may this person become freed from anger".
Perhaps you can sometimes 'turn it around' as well: instead of seeing the other person as angry, see them as not angry. If they didn't pull a gun on you or die of apoplexy, you could (possibly) think "that person is doing quite well at controlling their anger" as well as trying to root out the cause of that anger.
So 'metta meditation' might be a form of meditation to help inform "the causes and consequences of it". You mention that you were already doing that, i.e. "I felt more compassion for the fact that he was feeling anger". Maybe it would work to feel some compassion towards your own kilesas i.e. "may this person become free of conceit, delusion, doubt".
I guess that one of the worst things that could happen, a worst-case scenario, might be to welcome and to enjoy and to become attached to that arrogance: if you go around with the attitude, "I'm so great and good, because other people get angry with me and I skillfully don't get angry with them in return" and then because of that you're going around provoking other people to anger. So, instead, also avoid repeating the "not-so-correct maneuver" which provokes other people to anger.