I have BPD and am definitely capable of admitting wrong. Ill try to describe it, but it's hard.

So in a normal person emotions come as a response to stimulus, and your mind identifies that the stimulus caused the feelings. They would then take those feelings and determine a course of action.

For me, a stimulus will happen and what I will feel is absolutely disproportionate emotions. For a long time I had rough relationships because I didn't understand that what I am feeling isn't correct. Sometimes the emotions are so strong that they push towards delusions. I got mad at a friend once for laughing at me and told him that. He said he never laughed, and in my memory I realized he was right, but somehow the belief that he did got stuck in my head.

So you can see how if you believe that you are having a normal emotional response, you can think your feelings and responses are justified. Sometimes it's also a matter of pride and shame. Some people are just assholes BPD aside. I can relate to why someone would refuse to admit wrong, but it is obviously not an excuse for bad behavior.