It used to drive me nuts if someone was angry with me. I always act honestly, I always do what I feel is the right thing, so how can someone be angry with me? I need to immediately explain myself, tell the whole story of what really happened, and make sure that we’re ok. Now things have changed. I still act honestly and do what’s right, but I don’t respond with story.
If someone wants to be angry, it’s usually about them and not you. Sure, if you walk up and punch someone in the face then it might be about you, but things like that are (hopefully) very rare in your life. If it’s something that was likely a misunderstanding or misinterpretation and they still choose to be angry, then there’s just no reason to fight it by explaining yourself. You’ve probably found over time that explaining only adds fuel to the fire.
Is someone angry with you? Let them feel it and see what happens next.