Éowyn was absent from the battle at Helm’s Deep, entrusted instead with the protection of Rohan’s women and children, so the only knowledge she has of the fighting must come to her second-hand. But she’s confident in her ability as a rider and soldier and has no qualms about following Aragorn through the Paths of the Dead, even though she knows they’re likely to be fatal. Aragorn refuses to let her come out of love for her, but it seems he doesn’t fully understand her desperation to be useful in battle rather than in a domestic setting. Éowyn’s response implies that she feels belittled by the domestic tasks she’s been assigned all her life.