The Reason
Disclaimer – I don't own Naruto. If I did I would be living a life of luxury instead of studying.
As a child Sasuke liked to watch his brother train in the Uchiha grounds. He would sit on a rock and watch till Itachi left for his next mission. Then he'd try to mimic his brother's previous movements and "train" as well. His mother would look on from the kitchen and laugh quietly when he inevitably trip on his own feet and fall. His father would ignore his antics, deeming them immature and unworthy of his attention.
That was how he lived his early life:
Father ignoring him.
Brother having no time for him.
Mother too busy taking care of everything else.
Sasuke didn't mind. He was popular in school, regarded as an elite from a formidable clan, cooed over by the ladies and best of all, known to the whole village as the younger brother of the Uchiha prodigy. All was right in his world. Or so he thought.
He would never have believed that his brother killed mother and father if he didn't see it himself. As his brother's crimson eyes turned towards him, all he could see was blood.
Days later a traumatized Sasuke made a life-changing decision that will later cause the downfall of Konoha.
Get stronger
Kill
Ten years later, surrounded the ruins of Konoha, Sasuke finally fulfilled his oath and single-handedly ran a sword through his brother. As he stood over his dying brother, Sasuke couldn't resist asking the one question that plagued him since the massacre.
Why brother???
Itachi merely smiled, light fading from his eyes.
Because I can