Now just so everyone know, I've only watched the shows. I've seen every movie and every episode of Inuyasha. But I haven't read the জাপানি কমিকস মাঙ্গা so do not be upset with me if some of my thoughts are different.
I believe that Sesshomaru, at any point in time could have killed Inuyasha. Yes, their father did leave Tenseiga to Sesshomaru and Tetsusaiga to Inuyasha, making it futile for them to fight. But look at everything that happened.
In the early episodes, Sesshomaru used a human arm from Naraku and showed ইনুয়াসা the Wind Scar. He could've easily just used the Wind Scar on Inuyasha.