Here's the thing. She doesn't have anything to prove, but she is going to anyway. That's just her character. She knows she doesn't have to, but she still will just to show you that she can. Doubt her more and she'll prove she can again. We all already know this and you will too.
According to the caption on the bronze marker placed by the Multnomah Chapter of the Daughters of the American Revolution on May 12, 1939, “College Hall (is) the oldest building in continuous use for Educational purposes west of the Rocky Mountains. Here were educated men and women who have won recognition throughout the world in all the learned professions.”