Well, we're getting a bit ahead of ourselves. But he had given Arwen his *promise*; Aragorn and Arwen were engaged. (Have you read appendix A?)
Had Aragorn broken that promise, he would have been much less of a man-- and I doubt Eowyn would have wanted a promise-breaker.
I'm happier for all of them the way things turned out, aren't you?
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...down to the water to see the elves dance and sing upon the midsummer's eve.
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