Wow, I'm suprised to get such good responses (and in just one day). I thought that at least one person would flame me... And, by the way, no, I do not hate the pairing or either of the characters. They are my two favorite characters and I do think that they would match each other well; I only want a feasible explanation for a possible relationship.
Kikyou is Weak so that Sesshoumaru can be a Knight in Shining Armor
After walking for a few days, the group encountered a group of thieves (or a demon, but that doesn't really affect the storyline). For some reason, the thieves had enough nerves to not run away in face of a strong demon and a priestess. And so, Sesshoumaru and Kikyou fought the thieves while Jaken was ordered to take Rin away.
That was a completely stupid order since Rin would be so much safer under the protection of Sesshoumaru and Kikyou. But Sesshoumaru's only a few hundred years old; he's just inexperienced.
Anyways, the duo proceeded to fight off the bandits. Kikyou, despite being an almighty priestess who was able to kill every demon who attempted to steal the Shikon no Tama, was wounded one way or another. Some say she was too close. Others say that the bandits ganged up on her. Even others say that one of them threw a dagger or such at her and she was taken too much by surprise to dodge it (even though she managed one way or another to fend off surprise attacks for the Shikon no Tama). That's completely unimportant. What is important is that Kikyou got hurt and was kneeling down in pain or so.
Sesshoumaru, enraged that she was hurt (despite presumably having killed innocent women and children before) attacked the offending bandit and killed him in an instant.
Thus, he rescued Kikyou like a proper gentleman should (or gentledemon; whichever the terminology the reader prefers), regardless of whether or not she needed rescuing (again, she did fight and stave off demons for most of her life – that is, her actual life before becoming the undead). Although, of course, traditional knights in shining armor are supposed to save the poor maiden before she gets hurt, but who gives? This is a new wave of knights in shining armor. Or maybe that's just how they did it in Feudal Japan; let the lady get hurt and then the knight wins her favor by killing her assailant when she could possibly die in the next few hours depending on the intensity of the wound. It's absolutely perfect logic.