We might be jealous of Éowyn's life on paper (since she's the beautiful niece of a king, Théoden) if we didn't know how completely awful her life truly is. She is proud and strong, just like her brother, Éomer. The only thing she really wants to do is to fight for her country and to win honor with her sword. But because she is a woman and Rohan is a sexist place, Éowyn keeps getting stuck at home with the other women and children while important battles are being fought elsewhere.
And to make matters worse, her home isn't even safe anymore. Her uncle's court has been invaded by creepy Gríma Wormtongue, who has become Théoden's closest advisor. In addition to twisting and exhausting Théoden with his Saruman-powered advice, Wormtongue also keeps giving Éowyn long and frankly unsettling looks. Wormtongue wants Éowyn for his own, no matter how Éowyn feels about it (ick). And for a while there, Théoden seems too broken-down to protect Éowyn from his leering advisor. The months of this pressure on Éowyn can't have been good for her emotional health.
Luckily for Éowyn, Gandalf arrives at the court of Rohan about halfway through Book Three of The Two Towers to put a stop to Wormtongue's evil influence. Unluckily for Éowyn (depending on how you look at it), Gandalf brings Aragorn with him.
Éowyn takes one look at Aragorn and immediately thinks, that's the guy for me: "And she now was suddenly aware of him: tall heir of kings, wise with many winters, greycloaked, hiding a power that yet she felt" (3.6.72). Not only is Aragorn ruggedly handsome, but he is also "hiding a power that yet [Éowyn] felt."
Remember, Éowyn is a woman who feels like she does not have enough power. She isn't allowed to win honor for herself, and she wasn't able to stop Wormtongue from taking over Théoden's mind. Then, in walks Aragorn, looking hot and smart and powerful underneath it all? Of course she is going to fall for him—he has everything she wants.
Of course, you'll notice that, when Éowyn becomes aware of Aragorn (and quickly starts to swoon), she doesn't know him at all, really. She hasn't even talked to the guy. Maybe she has truly imprinted on him Jacob-style and maybe she hasn't. We'll have to wait for The Return of the King to see if Éowyn's one-sided love is requited.
In the meantime, we see what a complicated character Éowyn is. She's frustrated with her lack of power and she's crushing hard on a guy who is pledged to another woman (that part, Éowyn probably doesn't know yet). No matter how you look at it, her situation is not great.
We sympathize with Éowyn a lot, because her position among her people makes it hard for her to do what she wants to do. According to contemporary ideas, Rohan is definitely not a fair place for a female. But we are not so sure that the book wants us to approve of Éowyn all that much. Tolkien's narrator really keeps his distance, and nearly every description of Éowyn emphasizes that she is "cold." When Aragorn first sees her, he thinks:
Very fair was her face, and her long hair was like a river of gold. Slender and tall she was in her white robe gilt with silver; but strong she seemed and stern as steel, a daughter of kings. Thus, Aragorn for the first time in the full light of day beheld Éowyn, Lady of Rohan, and thought her fair, fair and cold, like a morning of pale spring that is not yet come to womanhood. (3.6.72)
In other words, Aragorn sees that Éowyn is beautiful (the guy's not blind). But he also thinks she is immature and unapproachable. She is "stern as steel" and "fair and cold." None of these terms make Éowyn seem very human. It's as though Tolkien disapproves of Éowyn's desire for glory (which is quite likely, actually, considering what happens to Boromir and the other characters who are too ambitious in these novels).
What makes this whole anti-ambition message unique and complicated in Éowyn's case, though, is that Boromir & Co. have to struggle with their own souls to find an internal balance between goodness and their desire for glory. Éowyn can't pursue glory in battle because of external reasons; she is a woman in a man's world. Power-seeking may be bad in this moral universe, but is it wrong to want the same amount of power that everyone else has? In other words, is seeking equality the same as seeking power?
The tone of The Two Towers' narration does not seem particularly sympathetic or warm towards Éowyn, since she's all pro-war and pro-glory (both definitely bad things in Tolkien's view). We'll get into this issue more in the The Return of the King learning guide, when Éowyn's story line really develops. For now, we'll just say: we seem to like Éowyn better than perhaps the narrator of The Two Towers wants us to. How about you? Do you feel like Éowyn gets a fair shake in The Two Towers? Are there ever times when seeking after power is morally justified?