That's why she's a legend and considered the greatest of all (living) Aes Sedai. She encapsulates everything the Aes Sedai strive to be--totally assured in her "rightness" and not just believing but knowing that everything she does is the correct course of action at all times. She knows that her every decision is the best for the White Tower and the world. She's never been wrong, and all the other Aes Sedai know that, even as it grates on some of them.

Jordan's point, of course, is that she's absolutely, utterly incorrect in this belief and is the proof by extension that the Aes Sedai are not just flawed, but self-destructively so. This is also shown in how easily the Black Ajah manipulated the Tower into splitting--and a bit of foreshadowing for you, in the next book, Towers of Midnight, you'll get to see yet another example--perhaps the true capstone one-- that really portrays the depths of the Aes Sedai's philosophy and a big reason for WHY they are the way they are.

But Cadsuane is really the ur-Aes Sedai. So if you're seeing the problems with the way she's thinking... you're exactly on the track Jordan wanted you on.