Family means the world to Lord Tywin. He wasn’t an overtly loving or expressive man except perhaps with his wife, but he placed a high value on his children and his relationships with them, especially as they brought more and more honor to the family name. Conversely, when they brought shame on the family or acted counter to how Tywin thought they should behave, he could be a monster. He was especially disappointed in Tyrion. His mere existence was a black mark on the family, and his actions throughout life only brought more embarrassment to House Lannister in Tywin’s eyes.
Tywin is as hard as he needs to be to get the job done, and he never does anything by halves. Coupled with his utter lack of sentimentality, he can be incredibly ruthless and cold but also highly effective. He is everything a feared leader needs to be: shrewd, cunning, courageous, and unforgiving. […]
[Joanna] died due to complications—complications Tywin blamed on his son, as if Tyrion had killed his mother on purpose. As well, Tyrion’s dwarfism was considered a disgrace, and Tywin never spoke in defense of his son."
He wasn’t an overtly loving or expressive man except perhaps with his wife
That sound of distant screaming you heard right now was me.
Conversely, when they brought shame on the family or acted counter to how Tywin thought they should behave, he could be a monster.
I love you, ASOIAF Campaign Guide. Tywin treated Tyrion like shit.
(Note that the wiki describes the Campaign Guide as a “semi-canon source” so make of these quotes what you will.)