In season one, we get a little spoiled by Ned Stark's affection and concern for his children, so Tywin Lannister's method of "parenting" is starkly different. Ha. Get it?
Tywin is especially cruel to Tyrion because of reasons that aren't even close to actually being Tyrion's fault. We get more backstory on Tywin's history of mistreating his youngest son when Tyrion tells Bronn and Shae about his first wife Tysha in season one.
Tyrion had fallen in love with Tysha at 16 and married her before realizing she was a whore Jaime had hired for him. However, when Tywin found out, he took the "joke" much farther. He had his guards have sex with Tysha one by one and pay her for each one while Tyrion watched.
When Tyrion finishes this story, the ever-candid Bronn says, "I'd have killed the man who did that." Fast-forward three seasons, and that's exactly what Tyrion does.
The circumstances surrounding Tyrion's murder of Tywin even mirror the story about Tysha. Tyrion is bent on revenge by the time he seeks Tywin out in the fourth season finale, and his rage is only magnified when he finds Shae in Tywin's bed. Tywin once again takes the woman Tyrion loves away from him and reduces her back to a whore right in front of his eyes.
