In truth, Cal is not technically a hermaphrodite, which is defined as an organism that possesses both male and female sexual organs and can act as either the male or the female in reproduction. Cal's genetic disorder is called "5-Alpha-Reductase deficiency" which means that Cal does not actually possess both male and female reproductive organs. At birth, he resembled a female (outwardly) but by puberty was discovered to have internal testicles and more testosterone than estrogen, which caused the sexual and emotional growth of a man. The word "hermaphrodite" as a being who is both male and female, here is used to describe that Cal was raised as a girl, but experienced a re-birth at puberty and became a boy.
When Callie goes to the New York library and looks up the word "hermaphrodite" the entry guides her to see the synonyms at "Monster." It is as if, here, Eugenides wishes to portray the message that perhaps there is a monster inside of everyone, but when embraced, it can be a thing of beauty.
Middlesex is full of other allusions (or references) to Greek Mythology as well. Cal, the narrator, frequently compares himself to Teiresias, a Greek character who was known to have switched genders in life, a genetic trait also passed to his daughter. Like the Greek god Hermaphroditus, Cal has the ability to empathize with and understand his ancestor's thoughts, making his story (and family history) more believable. These references to Greek Mythology, like the references to Greek culture, food, religion and humor, are not unusual considering the author and the protagonist of the novel are both Greek.