Disagree in context of the book, agree in context of motivational quotes. Distilling eowyn and "motivation" down to... being a woman? Lame as fuck. Being a woman is not what makes any woman great, is not where intrinsic worth lies.

But as to the quote being badass,

Context: you snuck into a fierce battle, facing your death and doom for the glimmer of hope if saving your world, when you see basically evil incarnate, a massive, powerful foe, strike down your beloved uncle who's basically a father figure to you and your brother. With fierce courage, maybe passionate stupidity, swept up in the intensity and absurdity of the hopeless battle you marched into, you put yourself between this foe and your dying uncle.

>'Begone, foul dwimmerlaik, lord of carrion! Leave the dead in peace!'
A cold voice answered: 'Come not between the Nazgûl and his prey! Or he will not slay thee in thy turn. He will bear thee away to the houses of lamentation, beyond all darkness, where thy flesh shall be devoured, and thy shrivelled mind be left naked to the Lidless Eye.'
A sword rang as it was drawn. 'Do what you will; but I will hinder it, if I may.'
'Hinder me? Thou fool. No living man may hinder me!'
Then Merry heard of all sounds in that hour the strangest. It seemed that Dernhelm laughed, and the clear voice was like the ring of steel. 'But no living man am I! You look upon a woman. Éowyn I am, Éomund's daughter. You stand between me and my lord and kin. Begone, if you be not deathless! For living or dark undead, I will smite you, if you touch him.'
The winged creature screamed at her, but the Ringwraith made no answer, and was silent, as if in sudden doubt. Very amazement for a moment conquered Merry's fear. He opened his eyes and the blackness was lifted from them. There some paces from him sat the great beast, and all seemed dark about it, and above it loomed the Nazgûl Lord like a shadow of despair. A little to the left facing them stood she whom he had called Dernhelm. But the helm of her secrecy, had fallen from her, and her bright hair, released from its bonds, gleamed with pale gold upon her shoulders. Her eyes grey as the sea were hard and fell, and yet tears were on her cheek. A sword was in her hand, and she raised her shield against the horror of her enemy's eyes.
Éowyn it was, and Dernhelm also. For into Merry's mind flashed the memory of the face that he saw at the riding from Dunharrow: the face of one that goes seeking death, having no hope. Pity filled his heart and great wonder, and suddenly the slow-kindled courage of his race awoke. He clenched his hand. She should not die, so fair, so desperate At least she should not die alone, unaided.
The face of their enemy was not turned towards him, but still he hardly dared to move, dreading lest the deadly eyes should fall on him. Slowly, slowly he began to crawl aside; but the Black Captain, in doubt and malice intent upon the woman before him, heeded him no more than a worm in the mud.
Suddenly the great beast beat its hideous wings, and the wind of them was foul. Again it leaped into the air, and then swiftly fell down upon Éowyn, shrieking, striking with beak and claw. Still she did not blench: maiden of the Rohirrim, child of kings, slender but as a steel-blade, fair but terrible. A swift stroke she dealt, skilled and deadly. The outstretched neck she clove asunder, and the hewn head fell like a stone. Backward she sprang as the huge shape crashed to ruin, vast wings outspread, crumpled on the earth; and with its fall the shadow passed away. A light fell about her, and her hair shone in the sunrise.
Out of the wreck rose the Black Rider, tall and threatening, towering above her. With a cry of hatred that stung the very ears like venom he let fall his mace. Her shield was shivered in many pieces, and her arm was broken; she stumbled to her knees. He bent over her like a cloud, and his eyes glittered; he raised his mace to kill.
But suddenly he too stumbled forward with a cry of bitter pain, and his stroke went wide, driving into the ground. Merry's sword had stabbed him from behind, shearing through the black mantle, and passing up beneath the hauberk had pierced the sinew behind his mighty knee. 'Éowyn! Éowyn!' cried Merry. Then tottering, struggling up, with her last strength she drove her sword between crown and mantle, as the great shoulders bowed before her. The sword broke sparkling into many shards. The crown rolled away with a clang. Éowyn fell forward upon her fallen foe. But lo! the mantle and hauberk were empty. Shapeless they lay now on the ground, torn and tumbled; and a cry went up into the shuddering air, and faded to a shrill wailing, passing with the wind, a voice bodiless and thin that died, and was swallowed up, and was never heard again in that age of this world

Tldr- it's a clever play on words Eowyn, represented consistently as an intelligent and thoughtful character, made in an absurd moment. Like you're on the brink of death, and a monster says "mankind can't kill me," but uses the word "man," so you jump in with a pun that kind of upends their confident statement. Fits with the wording of prophesy? Check. Why not? A lot of the magic and power in LotR is that of the magic and power of words and intent. This moment supports that wonderfully with a play on words and words and intent as an encouragement, that allows Merry to overcome his own fear, and leading to his ability to make a very helpful assist.

I think the movie actually ruined this moment. I can understand why you didn't like it in the movie. I was disappointed in it in the movie. It's everything in the book, even as someone who was sensitive to things that were too "girl power"-y when I first read the books.