Eowyn vs. Aragorn

[Quempel]

But if it wasn't something more, Aragorn could have simply just walked by nodded and went about his business. He did not have to stop and 'play' with Eowyn if she was nothing more than a silly girl playing with a sword. They were testing each other, plain and simple, not as enemies but to see each others stregnths.

If I were Aragorn I would want my better angles to follow me into battle. Maybe he knew Eowyn was the 'no man' that would best the Wiki and needed to know if she had it in her. Maybe Eowyn needed to know that the people of Rohan, if they fell, would have a place in Gondor. This is how these things are tested. Neither wanted the first warrior to crack going to war with them. They wanted someone who would stand up and fight, not run away in fear.

So even if Aragorn could best Eowyn he knew that he had her and the Rohirrim as allies. And vice-versa.