Mild spoilers follow for Asura Cryin' from episode 21, but they aren't very big, so you can read on unless you get really neurotic about that.
To set the scene, a griffon-like demon pops in and Aki comes out to fight it, dual-wielding katanas like a boss. Natsume, Takaya, and a few others stand off to the side, spectating. Because that is what we do in anime-land, when people are putting out tremendous efforts in death-matches we stand around and watch as if we are on our union-mandated break.
In any case, the griffon-thing is perhaps ten times the volume of Aki, and as she barely takes the upper hand in the fight Natsume comments (all this is paraphrasing, mind you), "She must have trained really hard to be able to do that", to which Takaya says, "A human can never be stronger or faster than a beast...".
For perspective, I am a 24 year old American, over-educated and well read. In the next part of this sentence, Takaya is going to tell us what advantage a human has over her bestial opponent. Throughout the Western tradition there have been two principal answers to that question. First is that humans have souls and God, which is silly, going out of style, and in any case not compatible with Takaya's non-Christian world view. The other answer, the answer I was expecting, is that humans are thinking animals, reasoning animals. There are perhaps a half dozen iterations of this from Aristotle to Ayn Rand, but at the core they all agree that a man can fight a tiger and win because a human can lay traps, can lure the animal, can devise tactics among a hunting party, can study the common reactions and behaviors of tigers and in the end defeat strength and speed with intellect. That is how Schwarzenegger beat the Predator. That is how the home alone kid beat the burglars. That is how the video game player can beat countless waves of video game enemies.
Takaya concludes the statement by saying "but she has more willpower. A human is more determined than a beast."
I think I can honestly say that in all my years, in all my reading, I have never encountered that perspective stated that bluntly as a legitimate philosophical position. And this is a belief that runs throughout all kinds of anime without ever being stated explicitly (though, in fairness, it is often alluded to). I have seen Naruto, though I stopped watching as the fourth ninja war arc got started, and I am not surprised to see determination and willpower praised as virtues, even high virtues. But to see it noted as the singular thing elevating mankind over animals is unexpected, to me, at least.
I see this as revealing a usually unspoken aspect of Japanese culture heavily represented in most anime. Of the big three, Luffy and Naruto are, for all their charm, heart-stoppingly moronic, and Kurosaki Ichigo is possessed of no more than moderate intelligence. Of the conventional heroes I can think of who were intelligent (a short list, but notably including Edward Elric, the Ghost in the Shell team, and Okabe Rintaro), typically we see the intelligence played down and kept in the background of the character, (Okarin, as always, standing as an exception). The Elric brothers use their prodigious talents to travel through the narrative, but win battles through willpower or simple power. There are a number of characters described as "battle geniuses", like Layfon from Chrome Shelled Regios, but often that genius does not extend past an intuitive understanding of battle.
The hero's team often has a smart or scientist character who is typically relegated to a purely support role. And every other villain is a genius, prodigy, or scientist. Typically their very brilliance makes them cold (as if anime writers consider psychopathy the rational course of action in our world) and leaves them without the greatest weapon, willpower or desire to win.
Certainly I have engaged in fairly heavy generalization, and certainly the degree to which it is represented in anime far exceeds the extent to which well-adjusted Japanese people believe in it, but anime is a medium very friendly to cartoonish extremes. I have no doubt this is not an original observation, but it is certainly one I, and maybe now some readers, will keep in mind for the future.
As a final note, I will leave you with a reminder that there are shows, typically more complex, intelligent ones, that do celebrate intelligence. Between Legend of the Galactic Heroes, Naoki Urasawa's Monster, and Stiens;Gate, we cover the entire spectrum of depressing to happy, active to slow, personal to grandiose with heroes triumphing through intelligence in more "Western" worlds where willpower is nearly impotent.