Tyrion Kills Tywin for Insulting a Woman He Just Killed
While fleeing for his life in the Season 4 finale, Tyrion decides to pop into the Tower of the Hand to pay his father, Tywin, a visit. He makes a pit stop along the way to kill Shae, the woman who cruelly betrayed him. In the very next scene, Tyrion kills Tywin for saying rude things about Shae, which, as you may recall, is a woman he himself just killed for being a treacherous douche. It makes absolutely no sense, and the viewer is left feeling like, "Well ... maybe Tyrion still cared about Shae? Even though he killed her?"
"Say hello to my little friend."
Amazingly, the only difference between the book version of this scene and the TV show version is a handful of sentences, which were omitted from the episode for reasons that cannot possibly be explained.
Before they part ways, Jaime reveals to Tyrion the truth about Tyrion's first wife, Tysha -- Tysha was not a whore that Jaime had hired to gaslight his younger brother, as Tyrion had spent the past several years believing. You see, Tyrion and Jaime came upon her after she'd just been attacked, and while Jaime rode off to annihilate the attackers (because he's Jaime Lannister), Tyrion stayed behind to comfort her, and they fell in love. They married in secret, and when Tywin found out, he had Jaime reveal to Tyrion that Tysha had been a whore the entire time, and the whole thing was a lie. Except it wasn't -- Tywin was so furious about the marriage that he forced Jaime to lie about it.
"We'll never have enough time to discuss all that! Now, let's talk
for five minutes about beetles."
So, when Tyrion confronts Tywin in that final scene, he's not asking about Shae -- he's asking about Tysha. Specifically, he asks where Tysha went after she was sent away, to which Tywin responds, "Wherever whores go." Tyrion says the equivalent of, "Me and this crossbow don't think you should use that word again," and Tywin respectfully ignores the suggestion, so Tyrion blasts him.