137th Gebirg wrote:

It seems to me that Jaime was the first to truly break the chains of his dead father's will and start to write his own personal destiny.
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I think Jaime was trying to do that prior to Tywin's death, but more recently the fact of his father's murder and his own inadvertent involvement in it-- "Tyrion loosed the crossbow, but I loosed Tyrion"-- has changed things somewhat. However you want to interpret Genna's line about Tywin and Tyrion, the interesting thing is that Jaime remembers it a couple times afterward, in a context that suggests he disagrees with and resents Genna's belief that he's not like Tywin. Now he seems to want to replace his father as much as to outgrow him.
Some of the most explicit stuff about Aerys and Joanna is in
A Dance with Dragons. Personally I think it's all a red herring-- I'm not big on theories where everyone is everyone else's secret relative-- but we'll see.