Even if we did survive and Mr. Tanaka adopted us, would my own family cease to exist? (3.2)
The fragility of Chiyo's family causes her stress and anxiety from a very young age. We barely know her with a stable family because when the book opens, her mom is sick and her dad is basically helpless.
They hadn't been born into the same family; but Granny had adopted them both. (3.90)
As our narrator, Sayuri must clarify that "Mother," "Auntie," and "Granny" aren't actually related by blood, but by the unusual geisha rituals that bind them together like a "family."
To learn in a single moment that both my mother and my father had died and left me, and that my sister too was lost to me forever…at once my mind felt like a broken vase that would not stand. I was lost even within the room around me. (8.63)
In our section on fate and free will, we mentioned the bad omen of the cracked pot. Here it returns. Sayuri is like the vessel, shattered by the loss of her family. Losing your entire family is an almost impossible ordeal to bear, and it's amazing that Chiyo is able to pull through.
When two girls are bound together as sisters, they perform a ceremony like a wedding. Afterward they see each other almost as members of the same family, calling each other "Older Sister" and "Younger Sister" just as real family members do. (11.2)
In addition to Auntie, Mother, and Granny, the geisha have a sorority-like system of having an older mentor and a younger mentee in a "sister" relationship.
When a man takes a mistress, he doesn't turn around and divorce his wife. (19.21)
The tragic implication of this is that a geisha will always be a mistress, which means she can never have a real family. She will always be on the fringes of other people's families, or within a family of other geisha that she made.
It goes without saying that this is why she adopted me. The fee for my mizuage was more than enough to repay all my debts to the okiya. (24.11)
You might be thinking, oh, that's nice that a geisha is able to build her own family. Many people consider their friends more of a family than the people they're related to by blood. But warm, fuzzy feelings are hard to come by in an okiya. The "family" is often in competition or looking to profit off each other.
Every day I lived with the Arashino family, I felt myself more in Nobu's debt. (29.1)
Sayuri lives with another family, not counting the geisha "family," twice: as a child with Mr. Tanaka's family, and as an adult with the Arashino family. Both times, she is only a guest, not a part of the family, and her stay is only temporary.
The Chairman wanted me out of Gion to keep me out of sight of Nobu, but he certainly wasn't going to marry me; he was already married. (35.5)
Even though Sayuri tells us flat-out that men don't marry geisha, she never once mentions the Chairman's marital status until now. Does this revelation, even though it isn't unexpected, change your opinion of the Chairman and his relationship with Sayuri?
As to the question of whether or not I really had given birth to a son of the Chairman's…if I had, I'd certainly be reluctant to talk too much about him, for fear that his identity might become publicly known. […] The best course, I feel, is to say nothing at all; I'm sure you will understand. (35.18)
As we said, it's tragic that a geisha can never have a family of her own, but it's heavily implied here that she had the Chairman's child. But because she is a geisha, she is forbidden to talk about her own son. Once again, the concept of family is ever elusive for a geisha.