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She believes he killed their mother
Cersei always assumed that Tyrion killed their mother just because she died while giving birth to him.
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Because of Maggy the Frog’s prophecy
Since childhood a wise woman made a prophecy about Cersei. She told her that someone would kill her and that all what she has will go to a younger and more beautiful woman. She always believed that the person who will kill her will be Tyrion.
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Joffrey hated him
Tyrion used to clash with Joffrey , Cersei’s son, a lot. Joffrey hated Tyrion and even tried to kill him once. Cersei saw Tyrion treating Joffrey badly and so she hated him more.
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He threatened her once
Tyrion once threatened Cersei and told her that he will take the things she loves. She concluded that Tyrion wanted to kill her siblings.
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Tyrion sent Myrcella to Dorne
Tyrion sent Myrcella , Cersei’s daufther, to Dorne to marry Trystane. Cersei felt a lot of pain because her only daughter was taken from her. She hated Tyrion for it. (See Why do the Lannisters hate the Starks?)
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He knew about her relationship with Jaime
Tyrion confronted Cersei indirectly about her relationship with Jaime Lannister. She hated the fact that he knew the truth and that he used to threaten her a lot.
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She believed he killed Joffrey
Cersei assumed that Tyrion killed Joffrey by poising him. She wanted him dead for it. (See Game of Thrones: How Olenna Killed Joffrey)
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Because Tywin hates him
Tywin hates Tyrion because of believing that he killed his wife. Tywin’s hatred was transferred to Cersei.
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She thinks he is a monster
Tyrion talked once about being hated for being a dwarf. Cersei might have hated Tyrion because of believing that he looks like a monster.
