I think what would make a veyr interetsing debate, would be to compare eowyn's behaviour to that of a teenager. Her wildness and motives do indeed resemble that of a teenager: a desire for adventure, a desire to proof yourself, a desire to have a meaningful life and make things better, a desire to break free from those who hold you back with rules. These are things teenagers deal with as well.
But Eowyn was hardly a teenager anymore, and she changes to fast that it could not have been explained as a simple proces of 'growing up'.
The teenager-eowyn link is interesting though.