Is it true that it's hard for people to realize their own faults?

Based on the outcome of this story.

Basically I did what some jellies suggested in the post today. I told the girl in my thread face-to-face that I wouldn’t pick her bag up because my parents didn’t allow me to interfere further, and if she wanted her bag then she had to come to my house and pick it up herself. She got quite irritated. She complained about how far it would be to get from the school to my house, and said a very annoying thing: “We have been friends for 3 years now, so what is so wrong in just bringing my bag to school for me? I have nothing to say about your parents!”

I got the feeling she didn’t realize she was the antagonist of this whole affair all along. She thought she was on the right side, she was the one who got bullied, and my parents (and possibly I) were the villains. In her mind it’s perfectly OK that she asked me to bring her bag to her house, but not OK that she had to go to my house to pick her bag up; and the fact that we were friend for 3 years could mean she could without hesitation asked me to carry her bag around waiting for her to show up, and my parents weren’t allowed to object to that. In short, she thought she was totally innocent, and we were so wrong.

It’s plainly her fault, but she never realizes it, even after the problem is solved. But now that I think about it, there are people who can’t realize their faults, even though everyone can see them. They are the only one who can’t realize their own mistakes.

So, is it true that it’s hard for people to realize their faults?