It’s a bit confusing at first, but there’s actually a legitimate reason. Why did Akaza break Tanjiro’s sword?
Akaza chooses to break Tanjiro’s sword out of embarrassment. He’s reprimanded by Muzan for taking a blow from a swordsman who’s not even a Hashira. He destroys the sword, vowing to end Tanjiro the next time they meet.
Tanjiro throws his sword at Akaza while the demon flees during the Rengoku fight. Akaza holds on to this sword, bringing it with him when he meets Muzan to discuss the battle.
Akaza meets Muzan to give a report
In chapter #67, Akaza meets Muzan to discuss the fight against Rengoku. Muzan is masquerading as a young boy with a chronic disease who can’t be exposed to sunlight. Adoptive parents raise Muzan, completely unaware of the boy’s true identity.
Akaza approaches Muzan through an open window. He reports that after an investigation, he is unable to confirm the existence of the Blue Spider Lily. The plant, explained in later arcs, is key to Muzan’s overarching plan.
Humbly, Akaza mentions that he successfully ended one of the Hashira. Akaza says this to ease the disappointment of not locating the Blue Spider Lily.
Unimpressed, Muzan unleashes an invisible gust of power that swings open the balcony doors behind Akaza.
Muzan asks why Akaza would bother to tell him that a “mere Hashira” is defeated. He says it’s only natural for a demon to defeat a human.
The annihilation of the entire Demon Slayer Corps itself, Muzan says, is the ultimate goal. Every slayer must be defeated so they may never sully Muzan’s sight again.
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The task of ending the Demon Slayer Corps is not complicated, according to Muzan. Yet, Akaza continually fails.
Akaza proudly reports that he defeats Hashira, but he leaves three other Demon Slayers alive. Muzan is angered by this fact, saying he trusted Akaza to get the job done.
Akaza chooses to break Tanjiro’s sword
“If you took a blow from a swordsman who isn’t even a Hashira,” Akaza calmly says, “Then Upper Rank 3 has indeed fallen.” Muzan and Tanjiro are familiar with one another. Tanjiro is actually able to recognize Muzan in an earlier arc.
With a sense of shame, Akaza leaves Muzan. While fleeing the Rengoku battle scene, Tanjiro throws his sword at Akaza. That exact sword is impaled through a tree outside Muzan’s home, apparently left there by Akaza before the meeting.
Out of anger and memories of being called a coward, Akaza breaks and destroys Tanjiro’s sword. Akaza says that he memorizes Tanjiro’s face and he’ll spill the boy’s brains the next time they meet.
So that’s the answer. Akaza chooses to break Tanjiro’s sword out of embarrassment. Muzan is disappointed that Akaza left Tanjiro alive while fleeing after the Rengoku fight.