She never accepts she is at fault!

My girlfriend has a problem with admitting when she does something wrong. This may sound like a trivial issue, but it’s not because it has serious repercussions whenever we have an argument about anything. She doesn’t even want to admit when she is at fault, which means I am always the one who has to take the blame even when I am not the one responsible. It makes me angry, resentful towards her, and I then start to question if this relationship is worth the effort. We have been together for two years and are thinking of taking things to the next stage, but this is the only thing standing in the way. I have told her this repeatedly, but she laughs it off and says I should accept who she is. What do I do?
If you can’t accept this, you should not. Trying to change someone is difficult and questionable, but an adjustment that has an impact on your emotional well-being and the future of your relationship should be non-negotiable. This is also critical for your future together because, as you point out, there are already feelings of anger and resentment that can only get worse if this isn’t addressed. If she doesn’t want to talk about it, she isn’t giving something that is important to you the attention it deserves. If she can’t find a way of fixing this, you may have to reconsider this relationship.

I feel trapped in any relationship and constantly want to be free. Then, when I am single, I want to be with someone. It’s frustrating and I don’t know what is wrong with me. How can I find a way of settling down without being my own worst enemy?
Why not avoid any relationship until you have had a chance to try and understand yourself a little better? There’s nothing wrong with being indecisive, but it’s usually a sign that you aren’t addressing something deeper. Start by thinking about what you want and why.