I'm almost positive it's about Rand having to work with women. At some point in tGS, he talks about how flawed it is because it needs two women to join with the one male, and that he didn't need another tie to others (need to re-read). I think it meant he needed to pull his head out and realize that trying to do everything himself was the flawed plan. The fact that there is an entire prophecy about the sword makes it obviously more important than a flawed creation to be cast aside.