I don’t think it goes that far, quite. Tywin certainly feels that Tyrion can contribute to the House by providing heirs – hence the marriage to Sansa. He just hates him as an individual and a symbol.
Different anon: if Tyrion had a legitimate son who is not a dwarf, do you think Tywin would consider making that boy his heir (after Joff dies and Tommen takes the throne of course)? or is his hate towards Tyrion so deep he wouldn’t even want his descendants to rule the West?
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