Jiraia wants Tsukuyo to be his Galatea, while he, Pygmalion. Let's talk about it.
Gintama's Red Spider arc is a fan-favorite for many reasons, no less because it provides important characterization and development for both Tsukuyo - a newly introduced cast member - and Gintoki - this is the first time audiences get to see his childhood from his POV.
The main conflict of the arc centers, of course, around Tsukuyo's relationship with her teacher. And many have analyzed the way it contrasts Gintoki's relationship with Shoyo. While yes, it is probably Sorachi's intention to draw parallel between the two in order to reveal chapter 1 of his MC's backstory more than 200 chapters in, I also think there's a lot more to be said about how VILE Jiraia's treatment of Tsukuyo is, especially upon viewing it as an example of the Pygmalion and Galatea motif.
Early on, Hinowa remarks that Jiraia fiercely protects Tsukuyo like one does for "an object they created." Which implies that in this pedagogical relationship, he sees himself not necessarily as teacher, but as creator, and she, his creation. She didn't "learn from" him, he MADE her, he BROUGHT HER INTO EXISTENCE (in his view).
Immediately, my mind flashed to the Greek myth of the sculptor Pygmalion who sculpted his "perfect" woman from ivory after being disappointed by real women. More specifically, in Ovid's account, when he saw women practicing prostitution, he began "detesting the faults beyond measure which nature has given to women."
And Jiraia DOES, in fact, detest Tsukuyo's nature - for she is born a woman. In them, he detests the idea that they are weak, that they have to be protected, that they rely on other people instead of toughing it out on their own. Never mind the fact that the men in Gintama also frequently count on each other and help each other out of a pickle, misogyny is one hell of a blindfold. And of course, he hates things typically associated with "femininity" like sentimentality, sexual and romantic desires - things that he clearly enjoys the commercial spoils of as he is seen patronizing Yoshiwara.
In "crafting" Tsukuyo, he constantly urges her to "throw away womanhood," which to him includes the aforementioned characteristics. For Jiraia, those are the "faults beyond measure which nature has given" her. Again, questionable because those things are, in essence, fundamentally human.
There is also a sexual dynamic in this story. By that I don't mean Jiraia is sexually exploitative of Tsukuyo - although a surprising number of Pygmalion & Galatea stories do end with the two getting together as a heterosexual couple. It is more about the possession of the FEMALE creation by the MALE creator - he deems her as a part of himself, and not her own being. He exercises control and power over her as her divine creator. (Creation by birth is a woman's thing, and is mediocre, but when a man creates life, it's magical, surely)
I like that Gintoki hints at a kind of impotence behind Jiraia's possessiveness over Tsukuyo. That he feels small, like a lone spider compared to her radiance. He wants to keep her to make himself feel more important. To shape her to his ideal so she was made to be his. But in doing so, he strips Tsukuyo of her humanity, her growth.
Luckily for Tsukuyo, she can walk away from that trauma with the people who sees no inherent fault in her soul, only features that makes her truly, uniquely herself. No longer someone's ivory statue, she is indeed her own person.
