It would be a mistake to think that Ichigo from Bleach is just another anime protagonist who has to conquer and defeat an evil version of himself because that is not what he is doing when he fights the spirit of his Zanpakuto: Zangetsu. While Zangetsu may first appear to be an agent of evil hellbent on making Ichigo's life more difficult, he is in reality a balancing force there to help Ichigo become stronger.
There is a reason why many Bleach fans mistake Zangetsu for an evil Ichigo: He is destructive, psychotic, and he looks exactly like Ichigo aside from his coloring. Indeed, when doing a side by side comparison with Ichigo and Zangetsu the two of them could be the two halves of the Ancient Daoist symbol of the Taijitu (yinyang). The visual reference immediately suggests that the two are what a Daoist would call a pair of inseparable and contradictory opposites (i.e. male and female, dark and light etc.).
Ichigo vs. Zangetsu
To further bolster the claim that Ichigo and Zangetsu are inseparable and contradictory opposites, it is important to understand what the function of their relationship was in Bleach's overall story. Zangetsu first appears after Ichigo gets beaten to a bloody pulp by one of the strongest fighters in the series: Kenpachi Zaraki.
The reason why Ichigo loses the fight initially is that he is paralyzed by fear, and refuses to accept help from Zangetsu. As Ichigo drifts in and out of consciousness he is dragged into his inner world, where Zangetsu is waiting to challenge Ichigo for the right to control his body. Zangetsu fights like a wild animal, in contrast to Ichigo's defensive style. He bullies Ichigo, taunts him, and exposes how little he understands about himself or his Zanpakuto.
Battle Ignition
On the surface Zangetsu still looks like just another roadblock in Ichigo's journey, but when they fight Zangetsu becomes whatever inseparable and contradictory opposite Ichigo needs to face to get stronger. When Ichigo is being a coward (Yin), and refuses to stand up to Kenpachi, losing confidence in his own abilities and the will to make necessary sacrifices. Zangetsu becomes recklessness (Yang), taking risks and being overconfident, making brash and unthoughtful decisions.
Ichigo is victorious in his fights with Zangetsu when he embodies the balance between these two inseparable and contradictory opposites at battle within himself. At the end of his first battle with Zangetsu he discovers what lies between cowardice and recklessness: courage. Ichigo takes the courage he gained in his inner world and uses it in the real world to defeat (or tie with) Kenpachi. Those who view Zangetsu as a mere villain or evil force are not seeing the full picture, because if a coward could just be a little more reckless they might just be brave.
Did Kubo Know What He Was Doing?
Kubo intentionally wrote Zangetsu and Ichigo as inseparable and contradictory opposites. Bleach is littered with so many other examples and references to Daoism, it would need to be a big coincidence for Kubo not to know about Daoist philosophy. The examples are both within the world of Bleach, like the Soul Society (an ordered society of laws and civilization) and Hueco Mundo (a chaotic world ruled by laws of survival), and within characters like Aizen (a forward-thinking ruler who desires change) and Kyoraku (a leader who wants nothing more than to uphold the world's balance and traditions). There are many more examples, and each case involves a pair of opposites who need each other in order to achieve balance.
Some viewers might disagree, and say that Kubo just made his characters good guys and others bad guys. Just because there are two opposing forces, that does not mean that they are "inseparable contradictory opposites" or tied to Daoist philosophy. These viewers could be right, but even if Kubo did not write Bleach's universe with Daoism in mind, his characters still have the ability to see themselves in their enemies.