In the book Glaedr said that Eragon must know what he was looking at, and Eragon saw Arya as an entirely separate person then from what he saw her as before. Then he manages to start fighting toe to toe with her because of that. Can someone explain to me how that actually happened? I may be wrong about the exact details of the first two sentences due to the fact I haven't read the book in a bit.
Eragon was told to start predicting her moves more, but was still basing it off what he though of her as the person he loved and less of who she really was. It took him some time, but he did eventually find a way to predict what she would do based off of who she really was.
It all works according the adage that if people don't know who you are or what you want, they will never be able to predict your next move. The above worked at a disadvantage for Eragon who just wanted to see the things, the way he believed in and this weakness made him much predictable. Arya on the other hand, was a master in it, and was easily able to read Eragon and defeat him in his own moves. It was when Glaedr, the golden dragon advised him to see through the veil of his opponents, know their true nature, predict them and then defeat them.