First you have to at least make an attempt to speak to them. Sometimes when you’re more willing to hear for the win instead of for understanding, that’s when things go left.
I have been the type that listened for the win. Once you get past who is right and hear people for their point it may make it easier to actually hear. Try that. I would take a break from the conversation too. Sometimes breaks help to put a pause and hold. A pause and a hold doesn’t mean you are ignoring the issue; it just means you want to give space and come back later. Breaks are sometimes necessary!!
One thing I would say is don’t ignore it altogether. Out of sight is never out of mind. Thoughts fester and can make things worse. Set a time to speak about the issues. If you can’t sit down with the other person, recognize what’s important. If maintaining a relationship is important you both not just one party will put in the energy. Don’t chase a person down to make amends. You don’t have to run and find a person to reconcile after adequate time as passed.
Also the severity of whatever happened matters. Anything that is about abuse, physical pain, or detrimental to one’s personal mental health sometimes can’t always be repaired but it is worth a try.
I wish you the best. I know arguments and fights are bound to happen in life. You can’t control everything that someone does but you can control your responses. Sometimes if you try and it doesn’t work, time will make it right and sometimes it won’t. Just try!