And this is, essentially, the ever relevant consequence of playing God. Especially with things that we don't fully understand o comprehend, as are the endochrine system AND neuropsychology.
Your explanation is overly simplistic, but you are not wrong that the systems at play are incredibly complex in ways we don't fully understand, and that there are innate behavioral differences that are more fundamental than socialization. This started out as an effort post disagreeing with you but as I was writing it turned into more of an explanation as to why you are basically right, but ehh I'm still gonna post it after my 30+ minutes of typing:
Hormones do not directly encode behaviors. They bias and tune motivational and salience networks through extremely complex feedback loops. Both androgens and estrogens affect neuronal potentiation in ways that make certain kinds of thoughts, emotions, or impulses more likely to occur, but it's highly dependent on context and environment, and the general homeostatic state of the body. The differences between men and women are very real, but they follow a broad statistical distribution and are highly plastic. You can think of sex hormones as biasing priors within a feedback loop system: developmental pathways shape hormones, hormones shape neural tuning, and experience shapes both hormones and neurons, in a feedback loop. The stable patterns that emerge out of this dynamic are similar enough across individuals to form recognizable averages, but a high degree of variance exists. Socialization does matter, it can have enormous effect in reinforcing and normalizing tendencies towards behaviors, but those tendencies have innate, undeniably strong biological biases in their distributions that is part of what makes humans what we are. No amount of socialization can undo that.
Both sexes produce both hormones, though in very different ratios obviously. But despite what troons and pooners think when it comes to talking about their "levels", the amount circulating in your blood is not what determines their effects on your body. While sex hormones do have some direct receptor activity (with testosterone binding to androgen receptors that influence energy, focus, and reward sensitivity, and estrogen binding to estrogen receptors that modulate mood, cognition, and stress regulation), the effect of changing them attenuates quickly as the body adapts to a new homeostasis. That’s why both andropause and menopause are associated with irritability. It has less to do with the absolute hormone level and more with the relative change from the body’s previous equilibrium. However, the other mechanism by which hormones influence behavior, that is much more pronounced, is genomic and developmental effects, and how these mechanisms actually work demonstrates the irrationality of HRT as modifying behavior.
Hormones are locally converted by enzymes within tissues, and those conversions vary depending on the tissue type. The locally converted forms then bind to receptors and exert specific biological effects. For example (and ironically), in many parts of the brain, testosterone is converted into estradiol, which is the active form that binds to receptors involved in synaptic plasticity, learning, and emotional regulation. In other regions, such as the hypothalamus and amygdala, testosterone is converted instead into dihydrotestosterone (DHT), a more potent androgen that activates genes related to aggression, sexual behavior, and metabolic drive, reinforcing classically masculine traits like increased motivation, vigilance, and competitiveness. These effects are not immediate, instead they reflect longer-term changes in neuronal potentiation and gene expression. In practice, men’s testosterone levels fluctuate substantially throughout the day without directly correlating to momentary shifts in mood, energy, or aggression. This long term genomic effect is
particularly important during prenatal development, when estradiol derived from testosterone helps masculinize neural circuits via DNA methylation, in ways that relate to motivation and reward. These effects build tendencies into the brain early on that can persist even in the absence of continued hormonal influence, especially as they become behaviorally reinforced over time. Having low testosterone, for example, does not necessarily make someone less aggressive or docile, because behavioral expression also depends on developmental structures and Hebbian learning.
Important to realize though, is that there isn't really a process like feminization as the equivalent opposite to masculinization. Female brains simply develop along a "default" pathway of human neural development that occurs in the absence of high levels of testosterone. This is why you can see things like androgen insensitivity producing outcomes that are behaviorally more statistically in line with females than with males. The effects that high levels of estrogens have on female brains is also somewhat different to the process in men, with effects being more pronounced in puberty than prenatally, and acting primarily as organizing and activating signals, promoting dendritic branching, synaptic density, and neuroplasticity in regions such as the hippocampus and prefrontal cortex, which are strongly linked to socially connected, emotionally responsive, and flexible motivation patterns, but crucially, this happen only in the absence of masculinization. This is important, because this means that estrogen in adult male brains does not magically undo the masculinization that has occurred in them. Pooners do begin masculinizing their brains a little bit, though only in a limited degree, by affecting gene expression in the brain (you can see a similar effect with PCOS), but troons taking estrogen does not "feminize" the brain in any way, because there is no mechanism that does that.
In a social sense, women and men do have an obvious yin-yang complementary patterning to their behaviors, but at a biochemical level that is not how we operate. As I'm sure everyone in this thread already knows, men are basically a template "female" human that is modified through specific chemical activation patterns that emerge from our genetics, but the causal mechanisms at play are not like a switch between two states.