Time
It was rare that Sesshoumaru hurried. When there was no danger, and his charges were safe, the pace the mighty lord would take was leisurely—regal.
This Sesshoumaru had time.
Why hurry when one had all the time in the world? He had so many years to do what he pleased. That was the true power, wasn't it? He had time. Riches would only last so long, and property was simply earth no matter how many times titles like ancestral territory were tacked onto it. But time went on forever, and the daiyoukai had it in spades.
Humans did not have so much time. Perhaps that was why Rin chose to run so often, even when they stopped to make camp. Rin would run to the fire. She would run to her lord's side to tell him she had cooked her dinner. She would run to the water's edge to wash. She would run to the flowers to greedily pick the happy ones. She would run to keep up with her Sesshoumaru-sama.
Rin did not have time to spare, and so she must run to do as much as she could before her time was up.
This was why when Rin came running for him Sesshoumaru would not stop. He would walk to meet her half way. Because though he had time to spare, she did not.
A few notes:
1. This originally had Jaken and Ah-Un in it as well, but I think it wasn't needed in the end.
2. The first Inuyasha fic I've ever posted. :D Whoo!