Tyrion asks for Casterly Rock - Game of Thrones S3E1
0Stripped of his position as Acting Hand of the King now that Tywin has arrived in King's Landing, Tyrion converses with his father over his position and wants. After unsuccessfully trying to get a "Thank you" for saving the city (which Tywin misinterprets as Tyrion wanting applause from the public), Tyrion explains that he is the rightful heir to Casterly Rock and the Westerlands, since Jaime, as a member of the Kingsguard, cannot inherit anything.
Tywin is infuriated by his son's statement, lashing out at the child he loathes with every insult he can come up with as he angrily refuses Tyrion's request out of the belief that his son is the embodiment of the worst of the Lannister who almost ruined his House, and anger over the death of his wife Joanna.