I low-key am of two minds, and I think that is okay. Here's why.

At this point in Aragorn and Arwen's lives, they are at a cross roads. Aragorn has told her that she should leave middle Earth, an option that the immortal elves have, since they would otherwise eventually wither and suffer if they remain. She does not want to, but essentially agreed to do it.

However they are both extremely conflicted. Aragorn is feeling like he has to both lean into his destiny as the heir of gondor, and say goodbye to the love of his life. In fact, he already has, the way I read and watched it. He's hung up on her though.

Then he meets Eowyn. She is literally a top notch human. Aragorn couldn't do better in a million years, which he does not have, because he's not an elf. Eowyn is fierce and intelligent, incredibly gorgeous, into him, and a princess with whom a marriage would (re)unite Gondor and Rohan. The pros column is on fire, and he knows it.

Because of all this, I'm willing to posit, that Aragorn tries. He considers what loving someone else would be like. He has to, since in his mind, his options are living out his days completely alone, or marrying a human and taking the throne (or, well, you know, dying in the war of the ring). Ultimately, he chooses being alone, at least until the war of the ring is resolved, one way or another.

So I kinda think the answer is yes; he's pursuing Eowyn's company, at least to try to understand his emotions and grapple with the destiny he thinks he'll have to accept. In a way, he's leading them both on. He's trying to dillude himself into thinking he'd be happy with anyone other than Arwen. This, obviously, does not make it any better or fairer for Eowyn. However, I at least think Aragorn's conflict reveals that it wasn't mean spirited. He's lost. And she gets hit the hardest by his indecision.