LotR -- Book 5 - Chapter 02 - The Passing of the Grey Company

[Lathriel]

In this chapter we get to see more of Eowyn and we get to know more of her feelings. Of course we already know that she cares for Aaragorn but now we also learn what she fears

"A cage,-to stay behind bars, untill use and old age accept them, and all chance of doing great deeds is gone beyond recall or desire."

(This is exactly what would happen if Sauron won.) Already Eowyn is stuck in one place and she is not given the freedom that she craves. She wants to be known because she hopes that this way she will also have more freedom and more of a say with what she wants to do, not what others want her to do.
But I do understand why Theoden wants her to stay behind at Edoras. He knows he can trust her and he knows that she will make the right desicions.
Those are som short thoughts for now. I'll probably post some more later.