Disclaimer- I don't own Inuyasha.
When Sesshomaru grew up, he, like many children, wished to be just like his father. Powerful, wise, strong, respected...
His father was everything a demon lord should be.
No demon dared infringe upon the honor or the land of Inutaisho. His father was impossible to control, to predict, to defeat.
And beyond that, his father had a good heart. He was kind to his son, kind to his wife, and merciful to even his foes.
His father could do no wrong.
Oh, the tragic innocence of children.
But as Sesshomaru grew up, he noticed, as all children do, the flaws of his parent. The way his defense of humans led to criticism and mockery from the other lords, the way his father would go to great lengths to defend others, even at personal cost.
Yet the greatest blow came when his father took a mortal wife. Such an insult, a disgrace he was to demons everywhere, the other demons whispered.
Sesshomaru defended his father, and was mocked. When he pressed these concerns to his infallible father, the great dog demon merely smiled gently, and told him that one day, he would understand.
But Sesshomaru didn't. He couldn't understand why his father kept a human woman as a consort, when so many demon women were readily available. He could not fathom why this emotion known as love was worth the loss of dignity and honor.
And that child... his half demon little brother.
To him, Inuyasha represented the crowning humiliation of his father, and the fall from grace his clan would suffer.
Sesshomaru would never forgive such a grand insult.
And so, Sesshomaru vowed to reject his father's ideals, his father's ways, and to become the greatest of all demons, the complete antithesis of his father's human-tolerant ways.
And in doing so, killed his own heart.
When Inuyasha grew up, he wanted to be a demon.
Oh, his mother told him it was fine to be a half demon, and supposedly, his father never saw him as lesser than Sesshomaru, his full blooded half brother.
But no one liked him because of his mixed, dirty blood. Demons considered him dirt, humans thought him a monster.
He was an outcast... a freak.
Not like Sesshomaru, the child thought jealously. His older brother was respected, feared by all. No one dared mock the great Sesshomaru.
To the half demon, his older brother was truly what a demon was. Cold, unshakable, indomitable.
And he was woefully, spitefully jealous.
It didn't hurt that the older dog demon seemed to loathe him in return, always glaring and whispering words of hatred and disgust.
So Inuyasha learned to hate back, to rise in anger and to snap at anyone who tried to hurt him.
And he vowed to become a demon, one greater than Sesshomaru, one greater than even his father.
Because then... just maybe, they wouldn't hate him so much. They would respect him, like they did Sesshomaru.
Oh yes, they would fear him. They would never make fun of him, or hit him, or hate him when he became a full demon.
Then he'd show Sesshomaru. Yes, he'd show his brother and everyone else.
I was speculating a lot for Sesshomaru and Inuyasha, seeing as how their pasts are shrouded heavily. I was going for a hopefully different outlook on why these two brothers have such a deep loathing for one another, a more complex one than mere blood. This was originally part of a much larger vignette, which involved much of the cast until I realized that these two had made their own story. Stupid dog demons...