Not sure most think "comfortable in your own skin" is to be taken literally.

StarAZ,

I was jumping the gun and providing what I figured would be the majority opinion on here...but not mine. 

They have cross-sexed neurology at the cellular level. That means having the wrong-sexed endocrinology causes progressive dysfunction,

It's not unknown for the patient to opt for the absolute minimal hormonal intervention, one that will cause a very slow transition over a decade or more just so their appearance will change slowly enough for them to retain things they hold dear - marriage, job, relationship wuth children until they grow up.

The dysfunction is progressive though without intervention, and the usual anti-depressants and so on can only deal with the side-effects of feeling one's mind slowly rot.

Here's a description of someone trying to "tough it out", to beat a neurological problem through sheer willpower, and what the consequences are:

Secondly, “Dysphoria,” defined by Marriam-Webster’s Collegiate
dictionary as “a state of feeling unwell or unhappy,” or in the American
College Dictionary as “a state of dissatisfaction, anxiety,
restlessness, or fidgeting” is simply too soft a word to describe the
angst most clinicians see on intake with this population. At best it may
be an apt descriptor for individuals who, despite strong evidence to
the contrary, are making an extraordinary effort to convince themselves
that they are sex/gender congruent. These individuals make life
decisions such as getting married and having children not only because
they may find it appealing to have a spouse and have children but with
the added hope that this activity will ease or erase their obsessive
cross gender thoughts. Although there may be instances where these
special efforts succeed, (i.e. the incongruity is mild) the more likely
outcome is a realization they have actually made matters worse.
Typically, at time of presentation these individuals report that either
their lives are in ruin, or they are very afraid that if their gender
variant condition was to become known they would loose all that they
cherish and be ostracized from family, friends and the ability to
support themselves. High anxiety and deep depression with concurrent
suicide ideation is common. One of the most extreme cases I have treated
was that of a 50 year old genetic male, married and the father of 3
grown children with an international reputation as a scientist who
reported to me that the reason he finally sought out treatment for his
gender issues was because the number of times he found himself curled up
in the corner of his office in the fetal position muffling his cry was
increasing. That is not dysphoria, that is pure misery.

It's not that they seek treatment just because they're unhappy: because they don't actually know the meaning of the word "happy" the way others do, they've never experienced that emotion. It's when they can no longer function, when the episodes become hourly instead of weekly or monthly.

I'm Intersexed, rather than transsexual, but my condition gave me cross-sexed endocrinology for much of my life, until it got better naturally, without treatment. So I know what it's like.

Usually there are body-map issues too, so surgical intervention is useful therapy. By then, the body has changed so much due to the hormonal treatment that the genitalia doesn't match the appearance anyway, is atrophied, and dysfunctional glands a cancer risk. Some surgical intervention is necessary. Most opt for a complete rather than "Barbie doll" reconstruction, but not all. Having a sex life is not high on their list of priorities.

Anatomically, they're Intersexed, partly male, partly female. The bit that determines gender identity is set to one sex, and other parts set to the other. The proportions vary, about one in ten have externally obvious intersex conditions too, as well as intersexed neurology.

So the "sex they're supposed to be" is exactly correct. Supposed by others who don't know anything about the biology, anyway. Supposed on the basis of external appearance.

When the external appearance changes, as it does in some Intersex conditions, these suppositions can change.

See for example this story from CNN:. These people  are protogynous pseudohermaphrodites. Born looking female, but masculinising later in life.Unfortunately, about 1 in 3 have a female gender identity due to their neurology, but this is usually ignored by society.

What is even worse is that we have made absolutely zero progress in the
treatment of spinal cord injuries for the past four thousand years;
modern neurologists are no better able to heal a spinal cord than Bronze
Age witch doctors.

Not so - some neural shunts have been devised, but are still in the labs. Progress is slow, but steady.

The first talk in this morning's opening Plenary Session was "Electronic
and Ionic Devices: Semiconductor Chips with Brain Tissue." Yes, you
read that correctly: brain tissue. For half an hour, Peter Fromherz of
Munich's Max Planck Institute for Biochemistry held a tough crowd's
close attention as he described his work on silicon-to-neuron
interfaces.
...
The brain is an interconnected morass of neurons.
Any comprehensive electronic interface with it would need not only to
have physical contact with, as Fromherz said, "hundreds of thousands or
millions of contact sites." But those sites would have to be stable both
in placement and biochemical interaction. You don't want them firing up
the wrong neurons, poking them destructively, or chemically interacting
with them in nasty ways, do you?

Fromherz cited three main
directions for hybrid-neuroelectronics research: neurosensorics,
neuroprosthetics, and neurocomputing. The first investigates devices
that could study the brain, the second focuses on creating devices that
could replace or supplement organic functions such as sight and hearing,
and the third explores using brain tissue to inform computing design
and function.

That's from the International Electron Device Meeting, 2008.