In reply to pietjepolo
Srry for length.
I have made a video analyzing her story arc on youtube.
Briefly my analysis is this: the way RT portrayed the event was not very good and did make it seem pointless.
However here is a more optimistic intepretation:
True Ozpin did mention protecting the tower, and the importance of the CCTS was probably well known. Problem with this alone is that not only would Pyrrha be up against Cinder-Autumn, (granted with some of her aura depleted) but also up against the dragon. Recall it was the Dragon that destroyed the CCTS tower, not Cinder.
As unlikely as it was that Pyrrha thought she could beat Cinder, no way she could think that she could also take out the Dragon, especially given Pyrrha's aura must have been partially depleted also given her fight with Penny happened less than an hour ago.
In other words, no way Pyrrha thought she could win.
Perhaps she thought she could defend the tower until help arrived? Plausible.
However, if you pay attention to her movement, her fighting style, the music and just the general tone of the scene, it was clear that she was not playing defensively. The smart thing to do would have been to act as a distraction, dodge & weave, and keep Cinder from doing any damage until help arrived. If you say this is a nitpick, let me point out that many times RT has emphasized subtle nuances in a character's fight style to show us what was happening in her mind (ie Carolina).
This leaves only one choice: life was no longer her concern.
When she went up that tower she had no interest any longer in staying alive. It explains everything about her actions, how she fought, how aggressive she was, and how she embraced death at the end.
She did not expect to win. She sought a warrior's death.
Now the question is of course: why? Why throw your life away when you had so much left to give?
It wasn't exactly rational, but it could make sense. If you pay attention to the deeper piety and virtuosity of the character. "For it is in passing that we achieve immortality. Through this we become a paragon of virtue and glory to rise above all."
By destroying Penny and playing right into Cinder's hands, she inadvertently caused all of the mayhem that was happening now. She had failed everyone and everything that she loved: Jaune, her team, the school, Ozpin, the people of Vale etc. All of the deaths caused by this Grimm attack were HER fault. (of course we forgive her in reality, but she wouldnt forgive herself).
This, combined with her sense of piety, that leaves only one option for her. Redemption through death. Die for your past mistakes, and become the paragon of virtue you wanted to be.
Her destiny was to die a warrior's death. To die like a huntress. After all recall what Torchwick said: "die like all the other hunters and huntresses throughout history".
This is what her destiny was. When she went up that tower she knew she had to die in order to fulfill it, in order to redeem herself and become immortal. When the flash of light happens when she dies, that is her soul going off to Valhalla (metaphorically).
So when she asks if Cinder believes in destiny, it was her self-actualizing and letting us know that this destiny is what she, Pyrrha, needed. Redemption through death. Passing and then joining the dead warriors of old.
It's poetic this way, unfortunately all of this subtext was either VERY subtle, or simply not there, or not build up sufficiently. As I see it this is the only interpretation that makes any sense, and makes her death resonant.