game of thrones - Why does Tywin hate Tyrion so much, right from Tyrion's birth?

In Game of Thrones S03E10, immediately after learning that...

Robb Stark has died,

...the following conversation takes place between Tywin Lannister and Tyrion Lannister:

Tyrion: ...it's easy for you to preach utter devotion to family when you're making all the decisions.
Tywin: Easy for me, is it?
Tyrion: When have you ever done something that wasn't in your interest but solely for the benefit of the family?
Tywin: The day that you were born. I wanted to carry you into the sea and let the waves wash you away. Instead, I let you live. And I brought you as my son. Because you're a Lannister.

Tyrion believes that his father's hatred for him is because he is a dwarf. This is evident from this statement from him to Jon Snow:

All dwarfs are bastards in their father's eyes.

However, dwarfism is not noticeable until the later years of childhood. There is no way Tywin could have known that Tyrion was going to be a dwarf. This is confirmed by this statement from Oberyn Martel from S04E07:

When we met your sister, she promised she would show you to us. Every day we would ask. Every day she would say, "Soon." Then she and your brother took us to your nursery and... she unveiled the freak. Your head was a bit large. Your arms and legs were a bit small, but no claw. No red eye. No tail between your legs. Just a tiny pink cock. We didn't try to hide our disappointment. "That's not a monster," I told Cersei, "that's just a baby." ...

So this confirms that although Tyrion had minor deformities on birth, his physical appearance was mostly normal. That's not a reason to kill your own child, even by GoT universe standards.

So what caused Tywin Lannister to hate Tyrion so much right from his birth?

Answer

One thing Tywin hated the most in the world was being laughed at since he endured that during his boyhood due to follies of his father Tytos Lannister. Yet once again, He became laughing stock of the realm when a malformed dwarf was born to him. To make things even more worse, the birth cost him his wife, Lady Joanna Lannister. Tywin never loved anything more than her.

He really explains why he hates Tyrion in season 3 episode 1, Valar Dohaeris when Tyrion asks for Casterly Rock and Tywin refuses it.

Tywin Lannister: I would let myself be consumed by maggots before mocking the family name and making you heir to Casterly Rock!

Tyrion Lannister: [quietly] Why?

Tywin Lannister: [raises his voice in anger] Why? You ask that? You who killed your mother to come into the world?

[Tywin stands and approaches Tyrion, while talking to him contemptuously]

Tywin Lannister: You are an ill-made, spiteful little creature full of envy, lust, and low cunning. Men's laws give you the right to bear my name and display my colors since I cannot prove that you are not mine. And to teach me humility, the gods have condemned me to watch you waddle about wearing that proud lion that was my father's sigil and his father's before him. But neither gods nor men will ever compel me to let you turn Casterly Rock into your whorehouse. Go, now. Speak no more of your rights to Casterly Rock. Go!

[Tywin returns to his seat. Tyrion is deeply hurt by his father's words, but says nothing. He stands and starts to leave]

So you see in above mentioned dialogue, following are the reasons why he hates Tyrion:

1. You, who killed your mother to come into the world? - Tyrion's birth resulted in death of Tywin's one true love.


2. You are an ill-made, spiteful little creature - He hated that Tyrion is malformed and does not fit the standard Tywin had for Lannisters - Being perfect and immaculate.



3. I cannot prove that you are not mine - Tywin suspected Tyrion is not his son but in fact a bastard sired by another whose name you can find in spoiler at bottom.


4. The gods have condemned me to watch you waddle about wearing that proud lion that was my father's sigil and his father's before him - Tywin hated that after all he had done to restore dignity to House Lannister, Tyrion once again made Lannisters a laughing stock by being born a dwarf.


5. But neither gods nor men will ever compel me to let you turn Casterly Rock into your whorehouse - He hated that Tyrion is into whores. He hated the fact that Tyrion married a "whore" in his teenage (Who actually turned out to be an innocent girl but Tywin deceived Tyrion that she was a whore.)


6. Speak no more of your rights to Casterly Rock. Go! - Tywin could not allow Tyrion to have Casterly Rock because in his mind Jaime was still his heir, the heir stolen by mad king. He also dreaded that seating a dwarf in throne of the Kings of the Rock would spell the end of house Lannister as all vassals would mock & defy such an overlord.

If you wish to read my analysis of how did Tywin Lannister turn into that bitter and awful man from Books perspective, see my previous answer here. It will help you understand many of the things why Tyrion was loathed by his father.

SPOILER:

There is a very convincing theory specially in light of release of TWOIAF that Tyrion is actually a bastard fathered by Aerys II Targaryen on Joanna Lannister.