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The key to analyzing Bucchigiri thematically is realizing two things:
1. fighting is not the only metric by which passion and worth and love are defined (something shown by Mahoro's personal strength/determination)
2. Arajin's rejection of Matakara is not out of disinterest or dislike, it is as a result of not feeling worthy of him
Despite all its pomp and spectacle, Bucchigiri is a show that cares deeply about how its details portray feelings beyond the superficial. Just by looking at how often Mahoro and Matakara are visually and narratively compared is just one such detail. Specific phrasing and word choice (in Japanese) is another, as Arajin distinctly uses impersonal as opposed to critical language when addressing Matakara (something the sub and dub ignore to varying degrees, often making his dialogue take on a harsher tone).
The biggest thematic takeaway from Bucchigiri is that you don't have to be the person someone expects of you to be loved by them. Arajin doesn't need to share Matakara's passion in fighting to be loved by him and to love him in return. And Matakara doesn't need to always be strong to be able to find some reason to live. He is worthy of other people's love just by being himself.
"Rather than pointless fights, I want promises."
This is the only part in the ending theme that is sung with two voices laid on top of each other and it encapsulates what Bucchigiri wants to say about its relationships. That the bond two people choose to share is more important than any pride you can leverage trying to prove something.