How do I overcome my hostility toward someone unwilling to admit they did anything wrong?

Let it go! Understand that it's not rational to believe that people always admit it when they're wrong. It also helps to be humble enough to admit to yourself that people have their own perspectives on things. It might be my opinion that someone is wrong, but I don't know every detail and am not in a position to be the final judge. It's a waste of time to try to get others to behave as I see fit. Carry on.
Forgive. You can practice forgiveness -- not to justify what the other person did, but to free yourself from the recurrent and painful experience of hostility. Takes a lot of energy to remain all tensed up and resentful. Forgiveness involves letting go of the hostility -- even if you decide to pursue the misdeed through legal means. Be well.
Supress. Suppression is a defense mechanism which entail" life has to go on and I will not think about it".
Detachment? We think about the importance of becoming attached 2 people. But we don't tend 2consider the survival value of detaching ourselves from those in our lives who r abusive, hurtful. Accepting their limitations can b exquisitely painful -as or more painful than grieving a death/losing a dream. I wonder what grief/sadness lives beneath ur hostility & what would happen if u stopped trying 2get rid of it.

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How do I overcome my hostility toward someone whey they are unwilling to admit they did anything wrong?

See Below. Need to know the nature of r/s to answer fully. You cannot change someone, but you can change ways you're dealing with that someone. Once you establish you can't change the other person, validate your own feelings to yourself, do deep breathing, relaxation. While feelings of anger are understandable when you feel you've been wronged, it's what you do with the anger and the choice is yours.