Moiraine was almost always wrong except on common sense issues for which the younger characters lacked the necessary knowledge to come to the correct conclusion. When you get right down to it, just about every plan she came up with was a variation on one of two elements "Run" or "Hide." Rand only gets really successful when he breaks away from her and goes off on his own.

Like most authority figures in the early series, or those whose tenure predated Winternight, she's a part of the System. The System is failing and falling apart. It runs a world that is threatened by dangerous foreign cultures and has no idea that it could be overrun any one of three different directions or how far from being able to right itself it is. The System is why mankind needs the Dragon Reborn to save it - they need someone who will completely shake up their society and civilization and destroy the System to free humanity in order to face the Dark One. Rand even hints in ToM that while he has an important part to play, humanity in general has to step up as well, and that he cannot do everything himself. His confrontation with Egwene is about manipulating events to put the general population in position to accept his changes and new order.

Moiraine is a part of that system, and it is entirely to her credit that when she surrenders and gives up everything to follow Rand, she is able to get some perspective on how flawed that system is, and even recognize her own attachment to it. She has been raised as a noblewoman and trained in the White Tower and has taken the social structure entirely to heart. While ironically she mentally chastises Siuan for being unable to accept the necessary destruction and hardships to come, she herself is just as guilty to a less degree. The difference is that Moiraine, having stepped partially out of the game to hunt Rand, is willing to write off a little bit more than Siuan, who has spent the last ten years seeing the world as something it is her responsibility and prerogative to arrange as she wishes.

From a narrative perspective, Moiraine is wrong so much because she is kind of the guide or spokesman for the world and society and the System, and all that has to change if Rand is going to win. He, like Mat against the Snakes and Foxes, can't win if he plays by the rules as they are set up. Unfortunately for Moiraine, she has lived her life relying on those rules, and thus her exposition and advice is framed in such a context, and shaped by her understanding of the same.

That's why she had to go.