Whatever it was you sure don't want to explain it too much.
Allowing yourself to make mistakes is hard. I have a tendency to beat myself up for things that don't even involve other people, so you can imagine how horrible I feel if I think it's harmed someone else.
Like you said to me it's a good sign that you are not whatever negative messages are being shouted at you. If you were, you'd just roll your eyes, and give the the old "whatever".
If someone is in your face and can't accept or forgive you for something, they might have something else going on, depends on it's a family member or friend or romantic partner, but I think the bottom line is someone feels they have the right to control you, and they feel that you are obligated to sit there and be criticized, long after whatever you did has passed.
If you feel you need to reassure this person that you know it was a mistake and that you are sorry, I would do it one more time IF you want---but I would be clear that this is the last time you are going to address this particular issue. If you are speaking from your heart and have genuine remorse, expecting anything else is just self-abuse. Stronger personal boundaries and just saying that you won't be talked to that way. Of course, when you do that, they're gonna test you to see if you really mean it.
That's the best I can figure from what you've said.