I hate to come off as a nymphomaniac, but...

[The Squatter of Amon Rûdh]

Absolutely, but, interestingly, he doesn't use language that she will understand.

Look at their last conversation before Aragorn leaves for the Paths of the Dead: there's no natural or convenient place where he could bring up the subject. In any case, he's talking about the practical reasons why Éowyn can't travel with him, which are completely legitimate given the circumstances: you don't just ride off with the King's relatives without asking. He's not missing the sub-text, or even clumsily avoiding it: he's just being tactful. Would it really have made Éowyn feel any better to hear about Arwen and how much he loves her? I think not.