These were the words spoken by Daenerys Targaryen upon meeting Jon Snow, after Jon reminded her that her father the Mad King Aerys burned Jon's grandfather Rickon Stark and his uncle Brandon Stark alive. By this point in Game of Thrones, it's a remarkable achievement indeed for any of our beloved cast of characters to have survived all the way to the seventh season, against all odds. So many other beloved characters have perished in the enduring strife of the great Houses of Westeros over control of the Iron Throne. It's important to note that many of the current survivors, like Daenerys, have done so by laboring to overcome the sins committed by their fathers. Daenerys becoming the "Mad Queen" - something that Tyrion and Varys are starting to fear - would fly in the face of one of Game of Thrones' most consistent themes.
Everyone in Westeros is a product of generations of familial conflicts. To be a highborn lord of a great house means amassing great power, while often striving for even more power, but this also comes at a cost. Even the highborn are pledged to their betters, and all are vassals to the Iron Throne - forced to fight in great wars that have decimated families and wiped out many great houses over the centuries. Being a lowborn is even worse; the common folk are always the ones who suffer the most whenever the wealthy and powerful play the game of thrones. The one bright spot that is beginning to emerge as Game of Thrones has launched into its endgame is the increasing realization of the main characters still alive that they are not bound by repeating the mistakes their fathers made. Indeed, most of the main characters in Game of Thrones have not only come to accept but are actively trying to prove that they are not who their fathers were.
Tyrion Lannister has struggled with his issues with his late father Tywin all his life - issues still not fully resolved even though Tyrion killed his father at the end of season 4. Tyrion came into the world doubly cursed: he was not only born a dwarf, thus deformed and unfitting to be an heir to the proud Lannister name, but his mother died giving birth to him. Since his first moment of life, the family painted Tyrion as having "killed" his mother, and neither Tywin nor Tyrion's sister Cersei ever forgave him for it. In terms of sheer intelligence, Tyrion is ironically the most like Tywin, one of the keenest minds and political strategists in Westeros. However, Tyrion spent most of his life indulging in his vices - wine and prostitutes - as a form of rebellion. Already tried and convicted by his father for the murder of King Joffrey - which he didn't commit - Tyrion's discovery that his father, who held his vices against him, was actually sleeping with his beloved whore Shea, sent Tyrion into a murderous fury.
Since aligning himself with Daenerys Targaryen, Tyrion has believed her when she says she wants to 'break the wheel' that has trampled the common people for centuries in the cause of gaining power for a few highborn families. Despite his reservations about her willingness to use her dragons to kill people and the possibility that she might one day succumb to madness like her father did, his efforts as her Hand have been to encourage her to be a kinder, gentler, and more just ruler. He wants to promote Daenerys' finer instincts and her desire to leave the world better than they found it. Tywin would scoff at such ambitions and subjugation of his family name, but Tyrion believes Daenerys will blaze a better way, not for the Lannister name, but for the future of Westeros.
In the grand scheme of things, Jaime Lannister proved an even greater disappointment to Tywin than Tyrion was, and Jaime does not care. Handsome, noble Jaime turned his back on his father's plan for him to become Lord of Casterly Rock early on. Instead, he dedicated himself to be Lord Commander of the Kingsguard and protecting whomever sits on the Iron Throne, because it keeps him close to Cersei, the Queen. Jaime has never wanted the things his father wants like money, power, and the ascension of House Lannister; for better or worse, the only thing he cares about in the world is his twin sister Cersei, the love of his life.
Meanwhile, it's Cersei - one of the worst people in Westeros - who strives to be the most like their father. For most of her life, her ambitions were never given proper form due to the restrictions Westerosi traditions placed upon her because of her gender. Cersei proved herself a master manipulator and behind the scenes string-puller, all the while chastised by people who hated her, like Lady Olenna Tyrell. In spite of the scorn she endured, Cersei delved deep into her father's playbook of treachery and murder, killing most of her enemies and ultimately securing the Iron Throne for herself, in defiance of everyone who ever underestimated her. Cersei would arguably be a happier person if she also rejected Tywin's ambitions, but she is driven to prove herself worthy of Tywin in the ways her brothers both fell short. Cersei should be the apple of her father's eye, yet somehow - even with ownership of the Iron Throne - it's easy to imagine Tywin would still constantly find fault with his only daughter.