I shall now present a thought experiment. For the purposes of this exercise, I hope you keep an open mind. I understand if your initial response it to reject the experiment, but if you let your mind go with it, you may find out something on a deeper level of your subconscious.
The thought experiment: What do you think would happen if, every single time you encountered a disagreement, fight, or argument with someone important to you, you took charge and steered the conversation (or silent treatment) towards a constructive solution; that you were the first to apologize, assume responsibility and fault, even if you really believed yourself to be the victim or completely innocent?
Being the first to admit you said something you didn't mean or something you could have left unsaid (even if you meant it) is freaking hard. It takes massive amounts of discipline and willpower to do it, regardless of who's to blame of the feelings hurt. You hear a voice inside you that says you shouldn't do it. The voice will tell you anything to convince you that you're the victim; that you're the one who deserves to be apologized to, not the other way round.
But guess what happens if you find it in you to ignore that voice (that's essentially Steven Pressfield's Resistance) and go apologize for your part in the fight? You get an unbelievable feeling of power over meaningless things. You realize you're capable of ignoring your pride and bitter animal instincts and rising above such petty things and, in a way, upgrading yourself to something more; almost to an Übermensch or a demi-god, if you will.
If you're able to do this once, you can do it again. And a third time. And soon enough, ignoring your useless (at the moment) pride becomes a second nature to you.
And you'll feel invincible.
Next time you find your feelings hurt after an aggressive conversation with an important person, try to shut down the victimized voice inside - at least for the experiment's sake. Be the first to make amends and apologize for your part. You may get a knot in your stomach at first, but see what happens next in your consciousness.