'No niggard are you, Éomer,' said Aragorn, 'to give thus to Gondor the fairest thing in your realm!'"
Then Eowyn looked in the eyes of Aragorn, and she said: 'Wish me joy, my liege-lord and healer!'
And he answered: 'I have wished thee joy ever since first I saw thee. It heals my heart to see thee now in bliss.'
This interaction is really quite interesting.
Eowyn's personal will is something that is a point of conflict between Aragorn and Eowyn. When Aragorn instructs Eowyn to stay, Eowyn asks why she may not do with her life as she wills it, to which Aragorn responds few are able to do so, and includes himself in that.
May I not now spend my life as I will?'
‘Few may do so with honour.'
However, Eowyn turns the tables on him by pointing out how his situation as a man is different to hers as a woman.
'Shall I always be chosen?' she said bitterly. 'Shall I always be left behind when the Riders depart, to mind the house while they win renown, and find food and beds when they return?'
'A time may come soon,' said he, 'when none will return. Then there will be valour without renown, for none shall remember the deeds that are done in the last defence of your homes. Yet the deeds will not be less valiant because they are unpraised.'
And she answered: 'All your words are but to say: you are a woman, and your part is in the house. But when the men have died in battle and honour, you have leave to be burned in the house, for the men will need it no more. But I am of the House of Eorl and not a serving-woman. I can ride and wield blade, and I do not fear either pain or death.'
She points out that as a woman, her will is never her own. Whereas need dictates what Aragorn does, how he responds to that need is for him to determine. His voice matters, his guidance is asked for, his cooperation is required. Plans are not made for him, as they are Eowyn. And while there are times a person has to be chosen to do something against their will, for Eowyn, that is her life.
Notably here, Aragorn cannot make a re-buttle. He has to shift the conversation towards Eowyn's fears, because he cannot tell her that her situation, the denial of her will, doesn't hinge upon her sex, as is proven by Aragorn himself later in the chapter.
"Then wilt thou not let me ride with this company, as I
have asked?"
"I will not, lady," he said. "For that I could not grant without
leave of the king and of your brother; and they will not return
until tomorrow. But I count now every hour, indeed every
minute. Farewell!"
He feels he needs Eomer's permission as well as Theoden's to let Eowyn ride with him. Theoden at least is Eowyn's king, she is hid subject and therefore owed authority over her, as with everyone else. Yet Eomer is not Eowyn's king, nor is she under his command as a member of his forces. In Aragorn's eyes, she is his sister, therefore she is his to command.
Despite Aragorn's efforts, despite Eomer and Theoden's lack of permission, Eowyn resolves to do as she will, and rides to battle, and she takes Merry with her, as she tells Merry;
“Where will wants not, a way opens, so we say," he (Eowyn as Dernhelm) whispered; "and so I have found myself."
These words are repeated by Theoden, after she and Merry defeated the Witch King, to the good of all. Eowyn embraced her will, and because of that, a great good was achieved.
Faramir doesn't need schooling as to the importance of Eowyn's will.
"Yet I will wed with the White Lady of Rohan, if it be her will. And if she will, then let us cross the River and in happier days let us dwell in fair Ithilien and there make a garden. All things will grow with joy there, if the White Lady comes.”
Where they go, the life they will live, hinges on Eowyn's will.
Eowyn herself we see take charge of her life.
'I stand in Minas Anor, the Tower of the Sun,' she said; 'and behold! the Shadow has departed! I will be a shieldmaiden no longer, nor vie with the great Riders, nor take joy only in the songs of slaying. I will be a healer, and love all things that grow and are not barren.'
She has chosen life over death, she will no longer seek death in battle or look for happiness only in war, but she will become a healer and help rebuild the world. None of this is contingent on anyone else giving her permission.
And Eowyn said to Faramir: "Now I must go back to my
own land and look on it once again, and help my brother in
his labour; but when one whom I long loved as father is laid
at last to rest, I will return."
No one gives her the order to leave Gondor, to leave Rohan, to return to Gondor, to return to Rohan. She is stating, without room for disagreement, where she is going and what she is going for, and on what terms she can return.
"I will" "I will" "I will". An insignificant phrase in itself, but for Eowyn, who has been told all her life "you will", to be saying "I will" at least is a significant shift in the power dynamics between herself and others.
Eomer is part of that shift.
"Faramir, Steward of Gondor, and Prince of Ithilien, asks that
Eowyn Lady of Rohan should be his wife, and she grants
it full willing. Therefore they shall be trothplighted before
you all."
Eomer, Eowyn's king and head of her family, does not speak of their marriage as something Faramir asked him for, and that he granted permission for. Eowyn granted it "full willing", Eowyn agrees, and "therefore" they shall be married.
But Aragorn doesn't seem to be in on the memo, hence the quote above. Here, he rather reduces Eowyn to an object, a gift, a fair treasure to be passed from one kingdom to the other. He calls her a thing, and comments on Eomer's generosity to "give" Eowyn away, when Eomer himself only spoke of the match in terms of Eowyn agreeing to marry Faramir.
Eowyn's response is friendly, but it's also direct, and in her response she makes a demand of Aragorn.
Then Eowyn looked in the eyes of Aragorn, and she said:
"Wish me joy, my liege-lord and healer!"
Rather a departure from the last time she asked something of him.
Then she fell on her knees, saying: "I beg thee!"
"Nay, lady,"
On her knees, begging, using terms of intimacy that he will not return. Desperate pleading met with dispassionate refusal. A use of "thee" met with a cold sounding "lady".
At her troth plighting, she looks him in the eye, making no show of submission or deference to him. She addresses him respectfully and with warmth, as her future liege-lord and as the man who healed her, but she isn't backing down or taking a submissive stance. She doesn't ask Aragorn to wish her joy, there is no "please", no "will you". She tells him, she instructs him, what to say, what to give to her.
She is centring herself, she is instructing Aragorn to direct his comments at her. Once more, she brooks no refusal.
It is direct, it is confrontational in manner, it is an order.
And he answered: "I have wished thee joy ever since first I
saw thee. It heals my heart to see thee now in bliss."
Eowyn gets what she asked for. Aragorn wishes her joy, and he uses "thee". Double win.