Y'know, when I was a kid and first read LotR, I never thought that Eowyn was putting aside a traditionally male role and taking on a traditionally female one. I wasn't quite sure what I thought about it, but looking back now (especially after having gone through years of therapy to overcome the effects of being born into a highly abusive family, in which the controlling parent didn't allow anyone to choose their role in the family, much less in life), things are clearer. Eowyn in Rohan was chafing under what she perceived to be a thankless role that was forced upon her, that of staying home and caring for Theoden while her brother rode off to the excitement and freedom and glory of war. I don't think she was bothered by the "feminine role," since she genuinely loved and cared for Theoden, and had apparently done enough as a strong leader to make the people of Rohan love and respect her, and want her to lead and help defend them in the absence of the king. In this, she shows that she has both leadership and nurturing qualities. It was the whisperings of Wormtongue that made her discontent, with her apparent lot in life, and in herself (as Gandalf points out to Eomer while Eowyn lies stricken in the Houses of Healing). I don't think the tale of Eowyn shows a contempt for feminism, or a belief that women should "stay in their place." I believe it's a little morality play of its own about the evils of heart and soul that befall a person when they deny who and what they are in their own right. By rebelling against her life in Edoras and desiring to ride away to war, Eowyn was denying the part of her that truly was a healer and nurturer. Wormtongue had made her think that these parts of herself were mean and worthless, that the only thing worthwhile in life was the glory of battle; it was another way of weakening Rohan from within, as Denethor's use of the palantir weakened Gondor from within. When Eowyn says she will be a shield maiden no more, she is making a choice free of manipulation, and accepting a part of herself she had been rejecting. She never says she will cease being a leader, but she has now had a taste of the reality of war, and glory won on the battlefield, and thus can now make a choice concerning the direction of her life that is based on experience rather than conjecture. She is no longer denying her true self.
Or maybe she just decided the grass was greener on that side of the fence.
