What societal and internal conflicts does Cal have in trying to determine his sexual identity?

In 2002, Jeffery Eugenides wrote the novel Middlesex, which became a best seller and Pulitzer Prize winner. The narrative follows the narrator and protagonist Callie or "Cal" Stephanides, who has 5-alpha-reductase deficiency, which causes him to have some female characterizes. This is commonly referred to as an intersex condition, typically brought about by incest, which was depicted in the relationship between Callie’s grandparents, who are siblings, and Cal’s parents, who are cousins. This Bildungsroman novel contains multiple allusions to Greek mythology.
Since Callie appears to the outside world to be female, she is raised traditionally as a young woman. After an accident puts her in the hospital, the intersex condition is revealed, and Callie changes her name to Cal and runs away from Detroit to San Francisco to live as a man.
Cal experiences a rebirth of sorts when he changes his gender identity. This internal conflict is summarized when he says:

I never felt out of place being a girl, I still don't feel entirely at home among men.

From a societal perspective, Cal was forced to combat the social constructs associated with gender. Dr. Luce classifies Cal as having a female gender identity because of a home video that shows Cal nursing a doll.
Society likes to create boxes to compartmentalize ideas like gender identity. This idea is reinforced when Cal looks up “hermaphrodite” in the dictionary and the entry includes “See synonyms at MONSTER.”

Cal is an intersex person—someone with mixed sexual characteristics that does not fit a definition of either male or female—with 5-alpha-reductase deficiency. Thus, by nature, Cal has both male and female characteristics. Biologically, he is of both sexes (in certain ways), but society fails to recognize the nuance of this sexual status. Though the condition exists, doctors, as well as the parents of sexually ambiguous children, often make judgement calls as to the sex of these babies at the time they are born. Rarely does society acknowledge the complexity of a mixed gender person's identity, as such a person clashes with our traditional view of human beings as being either male or female. This is at the heart of Cal’s conflict as he struggles to embrace who he is.
Cal’s challenge is not to choose between being male or female; though this is the choice society has conditioned him to believe he has to make. Instead, however, his challenge is to unify both male and female parts of himself, as that is the only way he can embrace his true identity. Intersex people are often pressured to conform to the world by living as one sex, but Cal is an anomaly and has to remain true to himself. He does not fit the definition of “normal” as defined by society, which makes the task of accepting himself much more difficult than it would be if he were clearly male or female. Cal lived as Callie, a female, for a long time, and he understands deep down that it is impossible for him to shed that part of his life as though he had lived it as a mistake.