It sounds like she is too proud, to admit her mistakes. She definitely is a perfectionist. She's probably very hard on herself...let it roll off your back...she likes that kind of interaction with you...know it and learn that is what it is...aggravating as it is...just let it roll down your back.
Her pride is really quite large...it means nothing, she's a critical person...she'll probably always be that way...but she never left, likes what you cook and still goes out with you to learn to ballroom dance...even took you to a company dinner...that says alot. That's compromising...