My take on what Inuyasha felt when he first heard of Rin, mixed with a combination of unsaid content missing from the anime. Let's be real here, if Sesshomaru thinks he doesn't deserve a satisfied/congratulations spiel from Inuyasha, then he has another thing coming.
Enjoy!
...
Inuyasha sensed him before he smelled, or even saw him. The air always seemed to thicken and his mood always dampened when his brother sought him out.
Sesshomaru.
He was surprised when he saw he wasn't alone this time. Accompanying him was a Kappa and...a human girl? He knew the annoying creature had been with his brother for quite a while, waving his two-headed staff around like he was invincible, but the girl he had never heard of. Sesshomaru despised humans, or him, at least. So what changed his mind?
"Who are you? We have the same hair and eyes, we must be related!"
"Filthy half-breed, you are the last person who this Sesshomaru would be assimilated with."
Ah yes, the very first time he had met Sesshomaru. The memory of their first encounter should have fired him up for a fight with his brother, but it had only resulted in making him sad. Sad? He didn't get sad, he got angry, hot-headed, impulsive, brash, but not sad. Or maybe those were all emotions he hid behind...
He cursed his human blood. Being void of emotion must be so much simpler, just like Sesshomaru...
"Inuyasha!"
Kagome's shrill voice brought him out of his thoughts and into the unfolding scene in front of him. His friends look concerned for their safety, but also somewhat for his; Sesshomaru was impassive as ever, Tenseiga already in hand.
"Sesshomaru is only passing by, let us not disturb him. We are on a mission as well, yes? We really should get going."
His friends stared at him incredulously, wondering what the hell came over him. Inuyasha was just feeling nostalgic, and sad, but made sure not to let his brother sense it.
"Have you finally matured since the last time we fought, little brother?"
Keh, you wish.
"Have you finally gotten over your indefinite hate of humans? Or was it fallacious all along?"
His brother growled, making the mood all the less friendly.
"I do not have to explain myself to the likes of you, Inuyasha."
"Alright, you as-" Inuyasha was not used to being in the presence of children, "you jerk. Come on gang, we have some jewel shards to catch."
He was getting away when his brother spoke once more, "Why do you stink of sadness? Has our encounter brought up some painful memories?"
Shit.
Inuyasha raced up to his brother, faster than the human eye could see, their challenging eyes only a hair's breadth away. "You know damn bloody well what's going on Sesshomaru."
Now curious, Sesshomaru decided to play his brother's game. "I don't suppose you would refresh my memory?"
Inuyasha snarled. "You say I tarnish your name through the mud, father's name through the mud, and yet you allow this human to join you?"
"What I do concerns you not-"
"I don't care what you do in the present unless you lack justifications for what you've done in the past."
"I don't follow."
"No, I suppose you don't. Well, you sure don't follow in father's footsteps. You're supposed to be honorable, and yet, all I see is a hypocrite."
His eyes narrowed. "I would watch my tongue if I were you. Who are you to compare father to me? You haven't met him and you certainly don't know anything of his character."
"Oh yeah? And who's fault is that?"
"I hope you aren't implying that it's mine because I'm not the one responsible for your mother's lack of teaching-"
"-My mother died when I was but a pup! If you couldn't take me in, why take her?"
"Rin is the first human who has not shied away from myself, instead, helping me in my weak, comatose state."
"And what, pray tell, is the big difference between her and me?!"
There was a pregnant pause.
"You really wish to know, half-breed?"
"Yes."
"You are half-demon, half-human, belonging to both and yet, to none. Demons sneer your way, and humans haul their pitchforks and insults in your direction. They fear you, and demons think of you like dirt. Your abomination ears and your unruly hair, your chewed nails, and your dirty fire rat attire; these are all qualities that even your human blood doesn't need to tarnish. And shall I start with your literate choice of words?"
Inuyasha was furious, to say the least. He quickly thought on his brother's words, 'Have you finally matured since the last time we fought?' and regained his composure.
"First off, you jackass, my ears don't come from my mother, that's for sure. They come from father, which means you had as much of a chance of having them as me. Secondly, maybe the reason I am so 'ungroomed' and 'illiterate', as you kindly put it, is because you didn't take me in, didn't take care of me, didn't teach me like father would have wished. Lastly, one day, everyone you care for, which is already few, will die. They will disappear, and you will be left alone, be sure of it. And when that day comes, you're going to wish you were kind to others. Kind to me. Because, Sesshomaru, the fact is, I am the only family you have. We're the only ones left. You might be immortal, but that only ensures a lonely life ahead." With that, the hanyou narrowed his eyes, an unimpressed scowl directed towards his brother. The latter, on the verge of retaliation, was cut off by a single clawed finger that was brought up to his lips. Inuyasha shifted himself closer to the other, leaning his mouth to his ear, whispering a hissed warning,
"I hope you're satisfied."