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[Game of Thrones/ASOIAF] Did Tywin mainly hate Tyrion because he's a dwarf?

I always thought the main reason was because Tyrion killed his wife and the dwarf/licentiousness behavior was secondary.
gpt
The death of his wife is absolutely the main reason. Tywin is a bit of a rarity in that he married for love, not power. His marriage had no political gain in it whatsoever, and he never remarried even though he was still in his prime when she died. Even if Tyrion had not been born a dwarf, Tywin would probably still have treated him worse than his other children, though probably not to as large of a degree, because he would see Tyrion as the thing that took away the love of his life.

The dwarfism ultimately is just a convenient reason he can give out, something that pretty much everyone would understand, whereas owing to how awful Westeros can be and how nobility is, if he gave the public reason as being the death of his wife there would no doubt be some people who say "Well, why not just remarry?"