Pretty much everything she said or thought had the undercurrent of, "Hmph! Who does Rand al'Thor think he is, giving orders. What, he thinks he's BETTER than me or something!?"
My favorite example of this is when Rand Portal Stones everyone to Rhuidean, and Amys is there to meet them. Egwene goes up to her expecting to be welcomed like the dreamwalker prodigy she is, only to be told, essentially, "be quiet, I have more important people to talk to, first."
Seeing her arrogance knocked back a bit.
While often she did have that undercurrent, I don't think it was pretty much everything she said.
One thing that she and many others did that got to me a bit, was these two trains of thought in short succession:
"He's acting a bit mad, I hope it isn't a sign of insanity encroaching"
"Why is he acting so stupid / arrogant / ruthless, I need to take him down a peg or two".
They seem to acknowledge he may be going a bit crazy (listening to FoH / LoC, I think the constant talking by Lews Therin, plus his issues with anger, show that realistically he was starting to have issues with sanity at this point), but then feel that whatever he is saying / whatever actions he is taking, he is doing in perfect sanity, and so must be an idiot / arrogant etc.
Possibly it was them trying to hide the truth from themselves....
