Campbell believed that myths were world-scale projections of Freud’s “nursery love triangle”. On that basis, he assumed that as girls and boys relate to parental figures of each gender differently, so would they relate different goals and procedures in the hero’s quest. The progression is logical, but the basis – Freud – is questionable.
Freud’s idea was, in a nutshell, that all children initially bond with a mother, who represents nurturing. Then, into this idyllic nusery scene of madonna and child, the father intrudes, representing an unknown and unfamiliar force. He represents protection, but since any good protector is intimidating, the child must learn that they’re on the same side in order to begin to trust.
Then, according to Frued, the challenge of maturation for boys is to transfer affection from Mother to an appropriate adult mate, and they achieve this by emulating Father in his protective role toward mother. In fact, like King Oedipus, they generally challenge the father at some point for the mother’s love. (Or, as a guy in junior high once wisecracked to me, “Man is born from the womb, and spends the rest of his life trying to get back in.”)
For girls, again according to Freud, the progression to maturation is more complex. The daughter must transfer affection first from the mother to the father, then to a suitable adult mate. This, he believed, was achieved by the daughter developing romantic or sexual feelings toward the father, then transferring them onto a mate.
Like most of Freud’s work, this theory is a starting point for deeper understanding. It’s an oversimplified model of the basis of human psychology. It was never intended to address what every individual experiences. For example, what of a daughter born to a stern, protective mother, and a nurturing father? What is her path to maturity? Even if you believe Freud’s model to be sound, you would have to allow for the variances when using it to predict what happens to someone whose history doesn’t follow it. Freud may have had the intelligence to make those allowances when he analyzed individuals. Unfortunately, his followers – including female ones – have a habit of transferring their own misogyny onto his ideas and warping them into “proof” that women must be stuffed into tight little boxes.
Campbell assumes that because Freud is dealing in archetypes, and myth is told in archetypes, he can just cut and paste without further analysis. From that unsound basis, it logically follows that a man’s heroic journey ends when he replaces his father as protector and embraces a female to cherish and protect, and a woman’s heroic journey… well, she doesn’t have one, but her journey to adulthood ends when she replaces her mother as the cherished and protected object of a hero.
The obvious flaw in the theory is that it assumes our world view is shaped more by our physical gender than by our experiences.
Think of people you’ve known well enough to armchair-psychoanzlyze and ask yourself: was their path to maturity determined by their background or their body? Consider a family where the father is an abuser instead of a protector. Or the mother is an abuser instead of a nurturer. What of parental incest victims, who are so often made to feel it’s their fault a parent wanted them sexually? Do the children even develop affections for the parents, which they would then transfer? Or do they develop unhealthy dependencies, which they must eradicate before they can develop affection for anyone?
It’s easy to think of exceptions to the rules in real life. Easier still to create them in fiction.
In writing a hero, there is absolutely no reason to consider gender. Despite how we’re taught to think of supreme ordeals as gendered (rape is for women, saving the family fortune/honor is for young men, etc.), anything can happen to anybody. Give your character a background and a point of view. From there, follow the logic to discover what their path to heroism would be. The paths vary as much between two women or two men as between a woman and a man, because the possibilities of human experience are infinite.
If you believe otherwise, then you miss the whole point of mythology and storytelling in culture: the finding of common ground in the most uncommon of circumstances.