Kagome (thinking): Inuyasha wanted to help the girl. I think he forgot all about making his sword stronger. And that explains why the spirit of Shiori's father helped him defeat the demon.
Remember your past, Inuyasha. You lost your heart to a mortal and ended under a spell for years. Coincidentally, you have no right to be part this battle.
The panther tribe of cat-demons attacked the west, and tried to conquer all other demons. But your father stepped in order to stop them. The panther tribe leader was an enormous cat-demon. Your father protected his men and battled the demons. Naturally, it was your father who emerged victorious. The demons who escaped domination by the panther tribe were extremely grateful. However, a cat's anger runs deep, and they cursed your father and his family for all eternity. And swore that they would, one, day have their revenge.
I would hardly call that a draw. You simply retreated in defeat.
TTaron
Now, now. You're one to talk, with all the men you lost. I wasn't nearly so determined back then as I am right now. Because now we have our master. Now, things are completely different.
Lord Sesshomaru! Lord Sesshomaru! I have searched everywhere for you! Inuyasha has surprised me. When did he become so powerful and learn to wield the Tetsusaiga like that?