if the thesis of pjo is the idea of yielding as a way of subverting fate, then you start to see it echoed everywhere. it‘s apt that percy is a son of poseidon and not zeus, bc it was poseidon who turned the tide of the war (literally lol) by bringing reinforcements to fight typhon, by listening to and trusting percy. poseidon had to let go of his control of the battle happening in his realm in order to help the rest of the gods, which was what ended up being the bigger fight anyway. sally had to be willing to give percy her blessing so he could bathe in the river styx, in order for him to fulfill his destiny, as it were. she very well might have been sending him to his doom, but she had to learn to let him go so he could take on his greater role. on calypso’s island, percy was torn between staying and leaving, again reflecting this idea of having to let go in order to fulfill something greater in the grand scheme of things (which, again, refers to percy’s duty as a hero). we also see his fatal flaw at play here, and how it could potentially jeopardise things. since percy forges personal connections so strongly & easily and values these bonds as much as his greater obligations as a hero—sometimes even more so—he would especially struggle with the choice of leaving ogygia bc his attachment to calypso equally counters what he knows is his responsibility to everyone else. he had to choose his battles, essentially.

really the whole of tlo is undergirded by this theme of subjective choice/desire vs. objective duty/obligation, which itself is the culmination of what percy has been internally struggling with the previous 4 books. even resisting the temptation to release the spirit of hope from pandora’s jar was an exercise in self-restraint, in not yielding. sometimes the right thing to do is to let go, and this doesn’t just apply to percy, it applies to the people around him, as well. annabeth had to find it in herself to admit that they needed rachel’s help, which was a crucial step in allowing them to figure out kronos’s scheme; ethan nakamura had to learn to redirect his sentiments and let go of his vengefulness, which was what luke had to do later on. percy had to force himself to leave beckendorf on the ship at the start of tlo so he would survive to fulfill his role in the prophecy, which was the thing that would ensure beckendorf didn’t die in vain. percy had to survive, to leave, to yield, to make his friend’s sacrifice count, no matter how much he personally hates it. the apollo and ares cabins had to let go of their petty feud in order to join the bigger battle against the titans later in the plot as well. like, it really all comes together when you think about it from this angle