How is San a "princess?"
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History is written by the victors.
She's the adopted daughter of Moro, god of the wolves.
Let's be bad guys.
She's clearly of high rank within the wolves, but not higher than Moro - who treats her like she's her own daughter. As they answer to Moro, San could therefore be considered the princess. But it's only Lady Eboshi who calls her a princess, as far as I can remember, so she probably just means it in a metaphorical sense.
She leads the wolves during the attacks.
Juliet Parrish: You can't win a war if you're extinct!
It's just a title (or nickname if you will) given to her by the other humans.
Much like how Elvis is the "King" of rock n' roll.