The interaction between patriarchy and gender is incredibly complicated, and there is always a temptation to reduce gender to patriarchal machinations. However, doing so leaves a lot of issues either unresolved or unexplained. An easy example is the seemingly constructive relationship people may have in the parodic performance, or even authentic appreciation, of gender-stereotypical behavior they themselves exhibit. The most obvious example for women is that of the use and application of make-up, the willing, even enthusiastic, desire and idealization of marriage. A willing attachment that seems distinct from their own abstract appreciation of the ways that patriarchy grinds women's lives to burnout and even despair. More obvious is the way in which such things reassert themselves even in the cultural production of the marginalized, or in sub- or counter-cultural production (e.g., transformative works of fandom). If feminism is as easy as convincing women that their forms of life are the product of patriarchy, such that they opt out, then the overwhelming conclusion many feminists would feel compelled to draw would be misogynistic, or perhaps more precisely meta-misogynistic.
Another puzzle is that of the place of queer experience within feminism, particularly top/bottom dynamics and the possible intersections of queer sex with S&M/BDSM. The lazy attempts at accounting for this is to simply accuse such groups, queer or hetero but kinky, of "internalized misogyny" or simply misogyny, or other such things, or to project the function of such acts for their participants so that the purported causes of such acts--patriarchy--remains plausible. But while the internalization of misogyny is something that can plausibly happen regardless, the explanation does not account for or incorporate self-narratives about these activities and serves to deflect from the need to explain how it is that this internalization would manifest under the specific auspices of sexual dynamics or otherwise assert themselves in a way abstracted from the imposition of roles on particular human bodies (especially if one considers oneself a "materialist feminist"). As well: why internalization of anything at all would be a requirement for these manifestations.
To me, these are signs that gender is more primordial than patriarchy, and is simply a tool or technology that patriarchy has weaponized. Patriarchy has swept in to become another contributing factor, another op-ed writer, another lordship and vassal, of gender. Meanwhile gender, like any actual technology would, thereby remains ambivalent in its relationship to patriarchy. But acknowledging this requires understanding what gender involves beyond the particularities of patriarchy or historicized socioeconomic institutions. It also requires not taking for granted patriarchy or such institutions, naturalizing them, and then building understandings of gender that serve their very own assumptions. Instead, the question to ask is a transcendental one: What makes gender in specific possible? What are the conditions of possibility for gender?
After all, what makes gender itself possible must also be what allows institutions and hierarchies that are gendered to be possible. Ontologizing gender through a psychoanalytic framework seems to be the closest method for answering this, and this is exactly what this book does by extrapolating something universal from the cisfeminine and transfeminine experience, which confront similar obstacles and frustrations yet seem to come at them differently. The cisfeminine and transfemme experiences with patriarchy serves to render more obvious and explicit the role of desire in the structural relationship between identity and alterity, even as this role is not contingent upon patriarchy as such and in fact generalizes to men. Under this framework, from the point of view of gender, patriarchy could be analyzed as, beyond just a material inequality, a set of sociocultural strategies for disavowing gender as an interpersonal anxiety or intrapersonal insecurity by displacing it onto particular sets of bodies that are to bare that burden. The book does not go into this, but I think its a natural extension of the main thesis: that gender is the psychic operation of evacuating the self for the sake and use of alien forces, for the assimilation of the "objectified self," i.e. the self image.
Patriarchy is partly the male disavowal of themselves as selves whose sense of self is constituted from without, by the desires or desiring of others, desires that operate and exist independently of them and their own control. It is a steadfast resistance to being desired due to mysterious causes and for mysterious reasons, and to desires from outside conditioning how they move about the world. Certain branches of feminism fall into a similar trap in the process of resisting or combating patriarchy, which would explain certain social movement contradictions.