Was Eowyn selfish?

I don't think that it's black and white. Eowyn is brave, Eowyn freaking kills the Witch King. Of course she is helpful in a fight.

But I think that, as someone else said, immature is a better word. Eomer is right: Eowyn really knows nothing of war. And not only does she know nothing of it, she WANTS it. She LIKES the idea of winning honor and glory through death. She does not understand that it is nothing to revel in until she had done it herself.

In one of my favorite parts of the book trilogy, Faramir and Eowyn have a lot of talks in the Houses of Healing. Perhaps the most important is when he at last breaks through her despair and doubt. She has been thoroughly traumatized, but he revitalizes her will to live, not by saying "let's go fight another war" or "let's go rule Rohan" but instead inviting her to marry him as Princess of Ithilian, where she says (and I quote):

"I stand in Minas Anor, the Tower of the Sun," she said; "and behold the Shadow has departed! I will be a shieldmaiden no longer, nor vie with the great Riders, nor take joy only in the songs of slaying. I will be a healer, and love all things that grow and are not barren."

I think she understood the gravity of the situation. There wouldn't be much of a point to ruling her people under the rule of Sauron, so she felt she needed to contribute to the battle as much as she could. Kind of an "all or nothing" situation. Just my thoughts.