"Then, Éowyn of Rohan, I say to you that you are beautiful. In the valleys of our hills there are flowers fair and bright, and maidens fairer still; but neither flower nor lady have I seen till now in Gondor so lovely, and so sorrowful. It may be that only a few days are left ere darkness falls upon our world, and when it comes I hope to face it steadily; but it would ease my heart, if while the Sun yet shines, I could see you still. For you and I have both passed under the wings of the Shadow, and the same hand drew us back."
Can we sit back and look at this for a bit?
Note how Éowyn is smiling, how hopeful she looks like. She has faith in him and believes it right to encourage Merry (and is correct in doing so, as we see in the end). She sees herself in him - someone who wants to fight, even if that’s unconventional.
Now look at Éomer. His expression holds no hope, only concern for this little hobbit who is so gleefully rushing into something he can’t even imagine. But Éomer knows. He has been fighting all his life, he has seen the weak and the innocent slain, and he knows how easily death can claim even warriors like Théodred.
Some people insist Éomer is a douche in this scene, especially for what he says to Éowyn only instances later. But is that the face of a jerk? I think not. Jerks don’t show that kind of concern for other peoples’ lives and well-being.
Éomer speaks what he knows. And he knows war and death and horror, the fact it’s not a laughing matter, and he wants to protect people from it - even Merry, whom he barely knows. He’s not a man of elegant and diplomatic words; he’s someone who watched his own father brought home dead and his mother succumbing to grief. He’s someone who was given one of the highest ranks in the land as a Marshal of the Mark at the age of 26. This is a man of war we are looking at, and from this point of view he is not wrong to tell Éowyn that innocents like Merry don’t have place in battle.
And when you look at that face, you might realise that in many ways he has as little hope as Éowyn herself.
Middle-Earth history meme » 1/3 Elves
She was proud, strong, and selfwilled, as were all the descendants of Finwë save Finarfin; and like her brother Finrod, of all her kin the nearest to her heart, she had dreams of far lands and dominions that might be her own to order as she would without tutelage. Yet deeper still there dwelt in her the noble and generous spirit of the Vanyar, and a reverence for the Valar that she could not forget. From her earliest years she had a marvellous gift of insight into the minds of others, but judged them with mercy and understanding, and she withheld her goodwill from none save only Fëanor. In him she perceived a darkness that she hated and feared, though she did not perceive that the shadow of the same evil had fallen upon the minds of all the Noldor, and upon her own.
Lord of the Rings in Black and White