Tyrion And His Father (End Of Book Tyrion Spoilers!)

[Tyria Targaryen]

2.) Tywin was going to let him take the black. We all know Tywin wasn't the best father, but it's not like he was going to kill his son. Even if this isn't enough reason for you, Then how about the situation in which Tyrion killed his father. Varys and Jaime had already freed him and given him passage to escape, he was home free. Why kill Tywin?

When Tywin told Tyrion that he was still planning to allow him to take the black (even after the trial by combat), Tyrion had a crossbow pointed at his father. Tyrion, I think, was skeptical that his father was telling him the truth. And frankly, why should he believe him - after having been condemned to death and sent to languish in the black cells?

If Tywin had volunteered that information to Tyrion while not under threat of death himself, his word might have carried some weight. But under the cicrumstances, I see no reason for Tyrion to trust that Tywin was telling him the truth and not just trying to save his own skin.

[Redtide6]

IMO Tyrion may had just been on his way to confront tywin about his relationship with Tysha. Tyrion seeing Shae in his father's bed is maybe what drove Tyrion to kinslaying.