So you and your girlfriend have been dating for about two years. For the most part, you enjoy her and have a good time, but whenever you have an argument like all couples do, she always seems to have the upper hand. Although you will usually admit when you are wrong, in her mind she’s never wrong and she will never admit it if she is. So how can you get your woman to admit her faults and treat you as an equal? The reality is that she is probably set in her ways and is not likely to change her way of thinking. A "Drama queen" like this has self-esteem problems and her ego simply cannot deal with the admission of being wrong. Her behavior may come from her deep-rooted insecurities, her upbringing, etc..
For women like this, to admit a defect is an impossibility in their view and they will do whatever is necessary, including insulting and even hurting people around them, to keep from seeing their own flaws or limitations. It is very sad for them and for the people around them. Women like this have psychological problems and unless they're in complete control, they will never be happy.
If you love her and really want the relationship to continue, you can attempt to sit her down and talk to her about the fact that your disagreements and fights shouldn't be about winning or not backing down, but about coming to a peaceful resolution. After talking with her about the problem, if it's apparent that she's not going to give in, you need to realize that she will never change and ask yourself the tough question: Do I actually want to marry a woman who will never admit that she’s wrong?
No matter how appealing her other qualities are, move on. You should be able to live a life filled with love, harmony and great communication with a high-quality woman who will respect and treat you as an equal.