Why did Mihawk spare Zoro’s life? Is it rivalry or a search for Yoru’s wielder?

SUMMARY

A One Piece fan theory claims that Mihawk isn’t a person but rather the physical manifestation of the sword, Yoru.
Yoru is out to seek the most powerful swordsman so it can finally have a suitable wielder.
The battles with Zoro and Shanks was to test out their capabilities as swordsmen.

Mihawk is a non-commital antagonist in One Piece. He does fight the Straw Hats but is not interested in a staunch enmity like other villains. He regards Zoro as his rival and is extremely curious to see him grow.

One Piece fans have considered him as a passive pawn who will come into play at the last moment, but it’s hard to determine whose side he will take. Yet, what if his passive nature is not a product of his disinterest, but because he is on another mission entirely?

A wild One Piece theory claims Mihawk isn’t even a human, and somehow the pieces fall into place.

Who or What is Mihawk in One Piece?

According to a fan theory, Dracule Mihawk is the physical manifestation of Yoru, one of the 12 supreme-grade swords in the world. Non-living things often have their own souls in One Piece. You can consider Going Merry, who was loved by the crew so much that she developed a soul of her own and her manifestation helped the Straw Hats on several occasions.
Shimotsuki Kozaburo | One Piece Chapter 1033
Similarly, the swords in One Piece also have souls. Shimotsuki Kozaburo, the swordsman who created Zoro’s sword, Wado Ichimonji, states that swords have their unique disposition, and a swordsman is the one who tames their wild nature to their will.

Theory is Mihawk is the son of Rayleigh and Shakuyaku. However, Kuja tribe only gives birth to females that makes Mihawk a real anomaly in the system.

Zoro called his Sandai Kitetsu a problem child because it always cut more than intended. Shusui is said to have a bad temper. Zoro’s Enma drains the Haki of its wielder. According to Kozaburo, cursed swords are only called so due to their owner’s inability to handle them. A sword also chooses its own wielder.
Zoro’s Three Sword Style | One Piece Fandom
Yoru is one of the rare supreme-grade swords and an extremely powerful one at that. It’s possible that the sword is on a quest to choose a wielder, and created a physical manifestation to aid its mission.

Why did Mihawk spare Zoro’s life in One Piece?

Yoru One Piece Fandom
Yoru is looking for someone who is strong enough to wield it, and it could have seen potential in Zoro. He is thus prepared to wait for Zoro to grow and become more capable. After all, what’s a better way to find a suitable owner than to test them out yourself? Thus, in their first duel, the strength behind the blow was controlled to leave Zoro wounded but not dead.

“It’s too soon for you to die. Discover yourself. See the world!! And grow strong, Zoro! However long it may take… I shall await you at the top. Strive with your whole heart and mind to best this blade, fierce one!!! Strive to surpass me, Roronoa Zoro!!!”

-Dracule Mihawk in chapter 52 of One Piece

When Mihawk saw the bounty posters for Luffy and Zoro, he was delighted. Readers interpreted it as the joy of a rival, but it could be because he could see Zoro growing.

Mihawk also had plenty of battles with Shanks, and it could be because Yoru found Shanks to be a potential wielder. However, Shanks never cared about becoming a swordsman and then lost his arm trying to save Luffy. Since the arms are the most important part of a swordsman, Yoru could no longer trust Shanks.
Mihawk with Yoru | One Piece Fandom
When Zoro bowed down to Mihawk for help, he was thoroughly trained. Why would Mihawk go to such lengths for two whole years, if he had no ulterior motive? In conclusion, Mihawk might be the physical manifestation of Yoru, who is sailing the seas in search of a partner. In the final battle with Zoro, Yoru might surrender itself if it is defeated.