Non of us choose who we fall in love with. It just happens.
Eowyn didn't know that Arwen existed. Aragorn never mentions her. The closest he gets to telling her that there is someone else in his life is when he comments that if he were free to choose, he would be in Rivendell, not Rohan.
Eowyn behaves as she does because she sees herself as a Shield-maiden.
For years, she's been lumbered with the job of nurse maid to her senile uncle and when the war starts, she has to take on the role of governing those of her people who won't be fighting when she wants to fight herself.
She falls for Aragorn, or rather her own image of Aragorn, because he's doing what she want's to do.
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