a matter of intimacy
Nanao knows that her Captain is far too well-mannered to touch her zanpakutou. Shinigami have their taboos, and this is one of them; to lay your fingers against another person's blade, against the essence of their will, is an act of intimacy, and without permission, it is a profound offence.
On her first day in the office, she felt his eyes lingering on it, and she knew that he was studying it.
After that, she wore it within her robes and ignored his pained silence.
She shields it from his gaze far more than she would shield her own body.
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