In A Feast for Crows, Genna (Tywin Lannister's only sister) and Jaime had the following conversation:
"Tired?" His aunt pursed her lips. "I suppose he has a right to be. It has been hard for Kevan, living all his life in Tywin's shadow. It was hard for all my brothers. That shadow Tywin cast was long and black, and each of them had to struggle to find a little sun. Tygett tried to be his own man, but he could never match your father, and that just made him angrier as the years went by. Gerion made japes. Better to mock the game than to play and lose. But Kevan saw how things stood early on, so he made himself a place by your father's side."
"And you?" Jaime asked her.
"It was not a game for girls. I was my father's precious princess . . . and Tywin's too, until I disappointed him. My brother never learned to like the taste of disappointment." She pushed herself to her feet. "I've said what I came to say, I shan't take any more of your time. Do what Tywin would have done."
AFFC - Jaime V
How did she disappoint Tywin?
From what I can guess it could be Genna's promiscuity:
It was hard not to feel contemptuous of Emmon Frey. He had arrived at Casterly Rock in his fourteenth year to wed a lioness half his age. Tyrion used to say that Lord Tywin had given him a nervous belly for a wedding gift. Genna has played her part as well. Jaime remembered many a feast where Emmon sat poking at his food sullenly whilst his wife made ribald jests with whatever household knight had been seated to her left, their conversations punctuated by loud bursts of laughter. She gave Frey four sons, to be sure. At least she says they are his. No one in Casterly Rock had the courage to suggest otherwise, least of all Ser Emmon.
AFFC - Jaime V
Tywin disapproved of such behavior and he would be very disappointed if he found a lioness of the Rock consorting with household Knights.
Or it could be that Tywin expected Genna to refuse to marry Emmon Frey but she ended up being persuaded by her Lord Father (Genna evidently never wanted to marry Emmon but for some undisclosed reason she did and even after they were wed, she never liked her husband) and therefore disappointing her lord brother. I can picture Tytos begging his daughter to save his honor by agreeing to the marriage and Tywin commanding her to protect the honor of the House by refusing. After all, on the wedding day, it was her choice that mattered, especially since her father was a weak man. If she chose her Father's honor, that would have disappointed her brother. Tywin was only ten when he objected to the betrothal, I doubt he would have given up without a fight when he was older and betrothal was turning into reality. But his sister choosing her father would put an end to any of his efforts.
She also angered Tywin once by saying that Tyrion was his true son, making him so angry that he didn't speak to her for half a year but I don't see how could that disappoint Tywin.
Has George ever commented on that other than "Keep Reading"? If he hasn't, "We do not know" or "No he didn't" are perfectly valid answers.