Akio is Sensei at the Takashi Koryu.  It is his techniques and style that will shape the next generation of Dragon Samurai.
Being his daughter, Kumiko was expected to be a superlative swordsman and a great Samurai for the clan.  When she reached the age of majority however and chose to become an artisan, many were shocked.  Her father was furious at first, and thought she was trying to shame him.
This quickly came to a head, Hagane was asked to challenge Kumiko and end this waste of talent.  The other Samurai asked for a duel to force Kumiko to choose the life of a Samurai Warrior over her dreams to create art and haiku.
Hagane stunned the entire clan by answering “I don’t have time to lose a duel”.
Hagane has never admitted any Samurai could beat her in one on one combat, she even told Uncle Mako she could defeat him in his prime.  To say she would lose a duel stopped 20 men in their stride.  “You’ve never watched her fight have you?  She can break Hiro’s Guard, she can cut through steel when performing the Tameshigiri test cutting for a new sword and she can cut an arrow in flight.  She has nothing left to learn, she is already among the greatest duelists of her generation.”
Nobody has questioned Kumiko since.