Disclaimer: I don't own Inuyasha.
Truth and Conjecture
When Suikotsu kidnapped Rin, Sesshomaru went after her…
When Suikotsu killed Rin, Sesshomaru didn't revive her. He let Kikyo bury her in the cold, hard ground, and he didn't look back.
Naraku, who knew Sesshomaru to be a calculating warrior, deemed it a strategic move on his part to be rid of the pawn that was used to manipulate him so often.
Jaken, who knew Sesshomaru to be a levelheaded thinker, believed he had finally come to his senses and realized that letting a human child tag along with them was ludicrous.
Inuyasha, who knew Sesshomaru to be a cold-hearted bastard, thought it was a testament to his cruelty. Sesshomaru could only think of himself, after all.
But when Sesshomaru walked away from Rin's lifeless body, ignoring the angry, pulsing protests of Tenseiga at his hip, it wasn't because he was being strategic, or sensible, or even cruel. He simply couldn't stand to see the look on Rin's face when she realized that he had failed her.