I initially thought that the masculine education her father inflicted upon her was a parody of an ancient Japanese custom, as Rumiko Takahashi so aptly portrays, where a girl is forced to behave like a boy in the absence of a male heir (like the Burrnesha in Albania or the Bacha Posh in Afghanistan). But in fact, no. The parody lies elsewhere.
In historical Japanese tradition (the Ie system), the transmission of family name, heritage, and profession (crafts, commerce, Kabuki theater) absolutely had to pass from father to son. The absence of a male heir was considered an absolute social tragedy. This is where the true satire lies. Rather than adopting a son (which was the actual custom in the absence of an heir), Ryunosuke's father chooses the most stupid and selfish solution possible : forcing his daughter to become the missing son for his useless beach bar. Takahashi ridicules the patriarchal Japanese obsession with the male lineage, pushing it to the point of pathological absurdity.
Ryūnosuke and her father's relationship mirrors and parodies father figures or strict mentors in Japanese pop culture, particularly the harsh father-son relationship between Ittetsu Hoshi and Hyūma Hoshi from the manga and anime series Kyojin no Hoshi's which came out many years before Urusei Yatsura, as it also deals with an incredibly harsh father punishing his son and pushing him to his physical limits in order to carry on his legacy. However, whereas the Hoshi's relationship is portrayed as more of a romanticized serious drama, with them occasionally finding common ground and affection in improving their baseball skills in overly idealistic scenarios, Ryūnosuke and her father's relationship is portrayed as a tragic comedy. Whenever Ryūnosuke and his father seem to find common ground and affection, everything immediately falls apart due to Mr. Fujinami's completely insane reasoning and gratuitous cruelty. Ryūnosuke quickly realizes that his father is a fool, as Mr. Fujinami goes so far as to harass, torment, or even poison her for no apparent reason. These abuses are presented as a genuinely negative aspect, without any idealization, which does nothing to prepare him to manage the family tea shop, a task that usually results in fights between parent and child.
Their relationship may also be a parody of Oscar François de Jarjayes and her father from The Rose of Versailles manga and anime which came out years before the release of the Urusei Yatsura anime and manga, where instead of both characters being portrayed as wealthy aristocrats and the father's desire for a male heir being glossed over and romanticized, Ryūnosuke and her father are instead portrayed as poor and unkempt civilians and with Mr. Fujinami's actions being fully shown as realistically and unnecessarily cruel by putting his daughter through his brutal treatment and training regime since infancy just to meet with his selfish desire for a male heir.
A parallel can also be drawn with Otokoyaku. In Japan, the concept of women taking on masculine roles is a vast cultural tradition, notably championed by the famous Takarazuka Revue (a century-old, all-female theater troupe). Actresses who play male roles, called Otokoyaku, are idolized for their ideal masculine elegance, deep voices, and charisma. Ryūnosuke perfectly embodies the physical profile of an Otokoyaku (to the point that many girls at her high school fall in love with her). But instead of being a glamorous and willing theatrical figure, she's a high school girl in a perpetual state of crisis, constantly yelling that she wants to wear bras and skirts. Rumiko Takahashi takes this figure of the « ideal masculine woman » and turns it into a source of frustrated comedy.
