The World of Ice and Fire covers this.
A later monarch, Tyrion II, was known as the Tormentor. Though a strong king, famed for prowess with his battle-axe, his true delight was torture, and it was whispered of him that he desired no woman unless he first made her bleed.
– The Westerlands, TWoIaF
Surprise surprise, Tywin named Tyrion intending to hurt.
Tywin for best dad.