I've seen Poasts dunking on annabeth for basically sucking at being the leader of the botl quest and with some credit to that point it is absolutely true that she messed up and made some bad/dangerous/questionable choices whilst occupying that leadership role i.e. her attitude in the sphinx scene perhaps being the most egregious offense, being not only an act of self-sabotage but an act that immediately results in the violent endangerment of her friends (see: hubris, specifically her excessive pride)
but to the point of annabeth floundering on this quest (never mind the immense psychological torment of the botl prophecy, which predicts "a child of athena's last stand" and a "fate worse than death" for a person she loves), I think it's important to note that the labyrinth quest was straight up impossible to complete in the beginning, and the same cannot be said of the quest for zeus' bolt, the quest for the golden fleece, or the quest to rescue annabeth and artemis. in this way botl's difficulty level is distinct from all previous adventures in the series. if a quest leader's role is to take charge and guide the direction of the quest itself then she absolutely could not have succeeded in that role because it's impossible to navigate the labyrinth without the aid of a god (i.e. hephaestus' spider, hera's blessings), ariadne's string, or a clear-sighted mortal. percy blows up in a volcano and grover and tyson go missing on annabeth's disaster quest in part because she simply did not have all of the tools she needed in order to succeed (hera even says to her face that percy holds the key to this quest, not annabeth; it wasn't without additional guidance that percy could even realize what hera was referring to)
the hopelessness of annabeth's efforts is something the audience can infer from the beginning, and it's the reason why percy expresses doubt in annabeth's stubborn commitment to her fruitless attempts at coordination. at one point she even resorts to using math as a navigation tool, to using numerical logic for a maze that defies all logic - she was desperate, but she really was trying. this is very in-character for her; we have more than a few in-text indications in botl that annabeth is at least subconsciously aware that she won't be able to figure out the labyrinth, but as shown in the sphinx quote, she's wisdom's daughter, and she won't shy away from a challenge and she doesn't want others to know that she's struggling. she's a perseverant girl even to the detriment of herself and others, and it wounds her deeply to acknowledge and openly admit that she's incapable of doing something, to admit that she requires the aid of another to achieve her goals (see: hubris)
so, incomes rachel to do just that, and annabeth loses her goddamn mind over it
her reaction to rachel is interesting because it's more complicated than mere romantic jealousy. just like the sphinx scene, annabeth's animosity towards rachel is, aside from her reservations about having a mortal on a dangerous demigod quest, straight up illogical behavior. everything about her unwillingness to let rachel on the quest is wholly inconducive to its successful completion. the issue isn't solely that rachel is a romantic rival and thus she doesn't want to be anywhere near her (though it is undeniably one core influence - the botl love triangles aren't just pointless drama, they're very important to the overall story); rachel essentially becomes the new leader and guide of the labyrinth quest, replacing annabeth in that role - annabeth, the girl who struggles with feeling important, who seeks glory and fame for her greatness, who covets opportunities to exercise her skill, all of which is evidenced by her character's desires which had been hitherto set up throughout the series:
^from the lightning thief
^from the sea of monsters
^from the battle of the labyrinth
so I love the botl quest being the one that annabeth of all people gets to lead because it's the perfect obstacle for her character. she wants to prove herself, she believes that she is capable of impossibly herculean feats and then the first quest she gets to lead is impossible to lead without the aid of the last person in the world she wants to accept help from. truly the best kind of conflict to throw at a character like her
and if we can go back to ttc and remember when athena looked directly into the camera and told us that fatal flaws are dangerous but can still be good in small doses then we can discuss the role of annabeth's hubris a bit more effectively. I bring this up because I've also seen people upset that annabeth isn't "punished" or condemned enough by the larger narrative for her hubris/that her hubris wasn't "corrected" or "overcome" sufficiently, and I see where this idea comes from but I think it overly conflates that which is the standard character flaw in general literature with fatal flaws (hamartia) as they exist in tragedies, especially greek tragedies and aristotelian philosophical frameworks
(mini-tangent: literary scholars have been debating over the meanings and purpose of hamartia for a hot minute and especially in the twentieth century and beyond; I won't get into it here but check the tags of this post for a tiny bit more detail on this if you're interested)
the fatal flaw is not necessarily constructed as a lesson that the hero learns from or a stain on their character that can and should be washed away with effort, it is better envisioned as an everlasting flame inside the body that burns and dooms the hero once it grows too large. notably this "flame" cannot be evicted from the hero's interior because it is so innate, particularly as rick employs said device in pjo: annabeth states that hubris is the flaw of children of athena, bianca states that holding grudges is dangerous for children of hades, as though their godly ancestry had predetermined their characters from the moment they were born. this has its root in the issue of the unchangeable nature of fate vs. the agency and free will of humanity that the first 5 books like to play around with
literary scholar ac bradley discusses hamartia in his famous writings on shakespearean tragedies - which are, yes, shakespearean, but I'm not going to waste time building a venn diagram to show the key differences and similarities between greek tragedies and shakespearean tragedies (feel free to google that if you're interested in this subject); instead let's just take a brief look at how he characterizes the dramatic literary device that is the "fatal flaw" (hamartia):
(if you're a shakespeare scholar and my mentioning bradley just sent shivers down your spine don't worry I'm very aware of his Flaws and using his readings sparingly)
"his weakness or defect is so intertwined with everything that is admirable in him". I'm going to bring this up again later so put a pin in this quote
you may have already noticed that I've said nothing about hoo or mark of athena so far and I think I have to disclose that this is intentional; there are many good reasons why many readers do not consider hoo to be a worthy successor to the first series. this post is not for my criticisms of rick's approach to fatal flaws and annabeth's character in hoo (though believe me I have plenty of those), so we're just going to ignore hoo with regards to discussion of annabeth's hubris here. back to pjo
botl is the book where annabeth's hubris truly sets fire to the page. her eventual acceptance/tolerance of rachel represents the beginning cooldowns of the worst effects of her fatal flaw. the most notable interaction where annabeth recognizes her own hubris and keeps it at bay is when she finally accepts in tlo that she cannot change luke or save him from his tragic fate. the death of silena and luke's role in that event is what finally cements this conclusion, something that she's been unable to accept for years, something that her siren vision in som told us she desired so extremely. she really believed that she'd be able to save him, as though she, once again, believed that she was capable of impossible feats like changing luke's fate (see: hubris!)
re: the issue of "is annabeth sufficiently corrected of and condemned for her flaws by the narrative?", I want to raise a counterpoint that might help reshape this mindset: do we believe that arachne deserved her terrible fate as punishment for her hubris? I don't even like the pjgg/pjgh books but percy himself sure didn't think so in his greek gods narration, where he tells us outright that he doesn't agree with the "preachy moral" of arachne's story:
so it's all the more appropriate that, towards the end of botl, percy expresses a really interesting idea that moves in conversation with pjo's overarching thematic commitment to breaking from the cycles of suffering seen throughout greek mythology and tragedies. do our flaws have to be extracted from our bodies? do flawed beings have to be punished like arachne? pjo lands on a more hopeful, freeing, and malleable conclusion: annabeth's hubris, like percy's own loyalty, can be maddening, it can be dangerous, it can be managed, and it is "so intertwined with everything that is admirable" in her
percy likens annabeth's hubris towards the sphinx to her ability to confidently defy the queen of the gods, even though hera helped out both of them significantly during the quest - because honor and subservience to the gods is not superior to either of their individual principles. in a more ancient tragedy or parable, they would have been punished narratively for this kind of behavior. annabeth can stand up for nico and go against hera, functionally her own patron goddess during botl, because of this stubbornness that's rooted so deeply in her identity. this scalding flame inside of annabeth doesn't need to be extinguished
