Wow Anon, this is a pretty big ask, but I am very glad you came to me with it.
You are absolutely right to suggest starting at ASoS because this is really where she starts questioning her own strongly held convictions. (I mean, her faith is shaken a little in ACoK but ASoS is really where the challenge comes).
First though: let’s quickly outline the way Brienne thinks about chivalry/knighthood at the outset of her journey. Of course, she’s incredibly naive, and most of her ideas about knighthood have been picked up fro the songs and tales she has heard as a child, which are much less messy than the reality of knighthood in Westeros. All knights are not gallant, all maids are not beautiful, and the sun is not always shining. She’s also pretty unaware of her class privilege, and her goal re: knighthood is very much based around Renly and his kingship as well as proving herself a worthy/capable knight in the eyes of the society that deems her a freak. Obviously she is a very empathetic person, and she cares a great deal about others (see her insistence on properly burying the tavern girls hanging on the river bank) but she’s pretty unaware of the realities of war and its effect on the common people. She is dedicated to knighthood but she is not yet a True Knight.
Of course, Jaime is a huge influence on Brienne in ASoS; I hardly need to say how much contempt she holds him in at the beginning, but his saving her from rape by the Bloody Mummers is a really key moment. I think it’s easy to jump straight to the bath scene and the bear pit but this is where she first realises that the world is not black and white. Jaime, a man she knows has broken oaths and attempted to murder a child, also saves her from being raped. It’a also worth noting that this is not only a kind and good thing to do, but it is a brave and knightly thing to do. Jaime puts himself at risk when he speaks up on her behalf, and a vital part of the knight’s code is to protect those who cannot protect themselves, which Brienne cannot at this point.
Obviously then we have the bath house scene and all that entails, which I think is pretty self explanatory: Brienne learns that sometimes one has to do something they would in another situation consider “unknightly” or dishonorable in the face of a higher purpose. Another important note here is that Jaime chooses the “higher” form of knightly vow here. He chooses to protect the common folk rather than the king, and he chooses to protect the common folk from the king. Once again, he is stopping the abuse of power, and disregarding his vows to his betters in order to keep the vows he made to the realm.
Then you get into AFFC and Brienne is being used by GRRM to highlight several themes. Of course there is the theme of knighthood and gender but Brienne also takes over Arya’s role (now that Arya is no longer in Westeros) of spending time among the common people and highlighting their suffering while the Tyrells and the Lannisters play at politics in KL. Septon Meribald plays a really crucial part in this when he talks to her about the broken men, and obviously Brienne despises such people but Meribald gives her a new perspective: not everyone gets a choice about whether they go to war. Brienne herself was all too happy to leave Tarth and follow Renly, but the common folk simply have to follow their liege lord into whatever slaughterhouse he tells them to.
Of course, she has also realised for herself the realities of killing, since she kills her first man early in AFFC. It is a moment of loss of innocence, but it is also a very self-affirming moment for Brienne. She remembers Ser Goodwin telling her that “you have a man’s strength in your arm, but your heart is as soft as any maid’s” and though he does not doubt her skill with a blade, he does doubt whether she could take a life. Here Brienne shows that she can take a life when necessary, and that her soft maiden heart is not an impediment to her knighthood.
So by the time we get to her final confrontation with the Bloody Mummers she’s pretty much at her peak in terms of Righteous Knighthood. When she steps out to protect the children against seven vicious killers she thinks she has “no chance and no choice” (have I mentioned that I fucking love Brienne of Tarth all right. I want this line tattooed over my heart). She has fully stepped in to the role of the True Knight, one who puts stock in her vows but also cares deeply for the common folk and the realm as a whole.
So now of course, what Brienne has learned is really being put to the test. It’s a popular theory that Brienne will kill Lady Stoneheart to echo Jaime’s killing of Aerys, and I think that is actually very likely. Brienne is going to have to choose one form of knighthood over another, and considering what she has learned along her journey, it seems backwards to think she would not choose to forsake a now-corrupt mistress in order to save Jaime and continue her quest for Sansa.
And because I can’t write Brienne meta without complaining about show!Brienne and D&D’s portrayal of her, should Brienne ever meet with Stannis in the course of her narrative, it is incredibly unlikely that she would choose to kill him. Because despite her vow to avenge Renly, killing Stannis does nothing useful, and would be detrimental to the realm, since (in my opinion at least) he is the best candidate for the Iron Throne. Brienne can kill if necessary but whether she could kill Stannis out of pure vengeance is debatable, especially now that she has had experience of the “real world” so to speak. Her view of chivalry is no longer what she imagined it as when she was a girl in Renly’s camp. I think that were she to see it now, she would recognise the emptiness of Renly’s chivalry.
Essentially, what Brienne realises over the course of the three novels is that knighthood is a much harder code to maintain than she had originally imagined. She swears her oaths with as much conviction as ever, but she knows now that some oaths are more important than others. She also knows that everything is not black and white, and she is not as quick to judge as she is in ASoS (though she is more wary). BUT what needs to be remembered is that although she becomes more jaded, she does not lose her faith in knighthood and chivalry as a concept. She knows now that knighthood is messy and difficult but still she strives to uphold her moral code to the best of her ability. What I find amazing about Brienne is her ability to see the horror and the reality of Westeros and not give up the fight. She is learning with astonishing speed how far to bend her own rules and when they need to be broken, rather than throwing the rule book out of the window, as Sandor and Jaime do. She loses her naivety but not her innocence and that is what makes her a True Knight.