What makes a man a man, and a woman a woman? According to the dictionary definition, a man is defined as ‘an adult human male’ and a woman ‘an adult human female’. The state of being male or female is further defined as possessing the biological characteristics of male or female primary and secondary characteristics.
So where does this leave an intersex individual? Specifically those with clear ambiguity as it pertains to those primary and secondary characteristics. A popular pseudo-scientific tale is that a person’s brain is somehow ‘gendered’, creating clearly distinguishable ‘male’ and ‘female’ brains (dimorphic). This is not supported by scientific findings, however, as covered by e.g. Joel et al. .
Even if this dimorphic split of the human brain into two distinct versions were to be fact, it would lead to many further questions, such as how a brain could have a preference for a specific configuration of primary and secondary characteristics. A much less complicated, and scientifically supported explanation for the differences between male and female behaviour comes in the form of the human hormonal system, especially within the interaction between oestrogen, testosterone and oxytocin  and the presence or absence of specific receptors in the brain.
Oxytocin appears to be one of the main behaviour affecting hormones, promoting feelings of comfort, safety, intimacy and bonding between parents and their offspring. Here testosterone appears to inhibit oxytocin , while oestrogen promotes its effects. The effect here can be observed e.g. by activity in the amygdala, which is found to be stronger in females, presumably due to those factors .
Similarly, the development of oxytocin receptors (OXTRs) is essential for social and emotional development and interaction . This demonstrates the intricate way that the neurological brain and the body’s hormonal system are interconnected. This includes in how these same hormones are involved in many aspects of the body’s operation, especially as it pertains to the body’s reproductive organs and physiological events related to them.
Looking at matters from this perspective, then, it seems rather clear that while the brain is neutral beyond the individual brain’s peculiarities, the hormonal system affects everything from mood to behaviour and beyond. This at least seems to confirm the core of the basic dictionary definition. With the primary sex characteristics setting the stage, the brain is then manipulated via the production of oxytocin and other hormones, along with their interactions and their ultimate effect upon the brain’s receptors, like the OXTRs in the amygdala.
Within this context, if we were to look at the aforementioned intersex individual again, a lot would thus depend on their overall hormone levels as to how they’d be affected. As for whether they’re male or female, the answer would be a definite ‘both’, due to the presence of both types of primary sex characteristics. Whether they’re happy with this state would be affected solely by environmental factors, not by any neurological or hormonal factors.
 Daphna Joel et al., 2015, https://www.pnas.org/doi/10.1073/pnas.1509654112
 Shota Okabe et al, 2013, https://www.sciencedirect.com/science/article/abs/pii/S0031938413001583
 Alexander Lischke et al., 2012, https://www.sciencedirect.com/science/article/abs/pii/S0306453012000339
 René Hurlemann et al., 2010, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6632777/