Gender is socially mediated, and constructed, as well as neurologically predisposed.  Innate qualities have to be qualities that do not depend on social interaction.  Consider the so called feral children known to history.  They are what people are like without social interaction or culture.  These children display natural predispositions to certain behaviors, with no cultural overlay.   Complex cultural behavior, dressing, eating with table manners, and much of what we call gender identity are unknown to them.

As a transsexual woman myself, I know how my brain works.  Right now in my life I live as and am accepted as a woman.  At an earlier time in my life I did my best to live as and be accepted as a male.  For me, personally living as a female requires less effort.  Why is this?  That is a question I stopped asking a long time ago and just accepted it as a mystery of human nature.    I now think that it all relates back to  a lack of direct physical aggressiveness + nurturing instincts along with how our culture sees such behavior.  Our culture equates masculinity with aggression and physical confrontation, and femininity with passivity and avoidance of such confrontations.  Perhaps the cultural prompt that it is female to be physically non-confrontational plays a role in shaping the earliest notions of self gender identification.

Complex human behavior is socially constructed.

Human behavior as we think of it is to a large extent socially  mediated.  The proof of this is the existence of so called "feral children".  These unfortunate individuals, were people who were isolated from a young age.  If you have ever heard the expression "so and so acts like they were raised by wolves,' feral children are the inspiration for that.  They behaved in ways that were inhuman.  Behavioral scientist, sociologist and psychologist determined that a person needs to be taught how to act like a person.  Very little of what we do is a pure primal instinct.  Most of our complex behavior is in fact learned and socially mediated. 

Gender, as a complex behavior, is no different than speech.  It is something that one learns from imitating other people.  Gender is socially constructed, meaning it is a behavior which has meaning because of the society people live in.  Consider clothing.  At one time in Mediterranean Europe, everyone wore a toga.  All toga's were basically the same, a mans' toga differing from a womans perhaps in the materials it was made of.   Consider jobs, like farming, among many non-European cultures farming is considered womans work.  In western cultures farming is considered mans work.  Those are examples of social behaviors that have nothing to do with innate abilities or instincts.

Gender identity is socially mediated.

Gender is also socially mediated.  What this means is that a persons gender is to an extent a matter of attribution by society at large. Society at large has ideas of what is male, female, two-spirit ... however many labels there are for however many genders that are recognized.  In our western society only male and female are fully recognized.  Everyone is often shoehorned into one of those groups weather it fits or not based on the biologically deterministic principle.  That is, that a person has a true, biological gender, determined at birth by their genitalia. Furthermore that the genital anatomy would determine their gender behavior.  In western society gender is understood socially as being set at birth.

Not all societies see gender that way. Many non-western cultures see gender as a matter of behavior, separate and apart from any anatomy of any kind.  For example in my own American Indian culture, (I was able to trace my most recent native identified ancestor to the Prairie Band of the Pottawatomie ), gender is something that can only be observed after a child has grown to a certain age.  Most boys grow up to be men, most girls grow up to be women however every once in a while a boy would grow up to be a M'netokwe.  Their behavior would be feminine to those around them, long before they began to dress in a female way.  Why is that?

This is where the brain comes in. 

There is a tiny part of the brain, the BNSTC,  which I and others believe controls gendered behavior.  Italiano will hopefully elaborate on this soon.

Either this part by itself, or more likely in concert with other parts of the brain is what predisposes a person to either the masculine or feminine role.  Since as I have discussed there is no way that wearing a dress or pants is an innate behavior it has to be something more basic.  Something more fundamental.  What I am about to say is something that will not be liked by some.  Yet  I am sure it is true.

Perhaps the BNSTc instead of controlling gender, influences a persons level of general aggression.  
(I heard a similar idea to this from a commenter on this blog.  They related aggression to sports.  I discounted that because plenty of women play "contact" sports.  i.e. many 100% gender normative women play softball, basketball, or other sports. )  A predisposition to aggression, and domination, for a young person to play rough and throw a ball at/to other people can be a neurological thing.  While other people could be predisposed to nurturing, to being relatively passive, and submissive. 

I know not all women are passive, but a predisposition to a passive social role could explain why some boys seem feminine by the standards of many societies.  By the standards of many societies, men are supposed to be more aggressive than women.   In many societies women are expected to be more passive, than men, to be nurturers.   Those are things which can be and are mostly instinctual behaviors.... interpreted into the beginnings of male or female gender identity.  Society takes over from there to either reinforce or discourage that
persons natural predisposition.

In the case of transsexual/transgendered persons...

In the case of transsexual or transgendered persons the predispositions are so strong that the discouragement or reinforcement of society at large cannot keep them in a normative role.  In western society thisgives us what we know as transmen and women. 
What I have said here has not made mention of sexual orientation at all.  There is a correlation according to multiple independent studies between aggression and sexual orientation in males. Similar studies relate physical aggression to gender identity.  These are findings that cannot be ignored, and paint a complete picture of the transsexual condition.  The same is true of studies which relate gender to neurology, or sexual orientation.  To have a complete picture all of those aspects have to be combined.  

Transsexuality is not 100% neurological, it is not 100% psychological, it cannot be explained solely as a function of either sexual orientation or gender identity as our society thinks of those terms.  Like most real life phenomena transsexualism is a pehnomena that cannot be explained in the length of a slogan.  Gender identity and sexual orientation need to be forgotten as terms of science.  What is scientific is to speak of predispositions, and social constructions, instincts moderated by social training, along with their complex interactions.

A person on this blog site calling themselves cloudy wrote of the idea that love of sport and implied aggression were the key.   While I still think that's a little off, it was close.  Plenty of women like sports, even contact sports.  However it is not as common a predisposition as it is for men.  Plenty of men nurture their children, but it is unfortunately not a common enough predisposition.  The above ideas I think will cover most people quite well.