The issue here (to me) is the insistence of pitting one answer against another; always making drama and arguing that it's "either this / or that" in perpetuity for the sake of arguing more than anything else. Like most apparent contradictions in life are matters of degree of difference, this again is some from pile A, and the rest from pile B. It's both. I'm sure that's not very satisfying to whoever wants to keep beating their particular drum, and sorry about that, but it'll also be infuriating that I don't intend to "back that up" either. That's my whole point: it's not an argument in the first place. This perspective could be a viable offramp, defusing the endless controversy, making both sides content and to drop it, but it won't, they won't. It's like politics. Well today's politics or spirituality where tribes insist on taking a side and fighting to the death, not about what makes most sense. Although as far as spirituality goes I'm more comfortable not believing in it, but mostly just not talking about it because you can't argue with people about politics or religion when they don't even have one foot in the real world. How we deal with gender issues at least has some foundation, and the main reason people run into trouble with it is when the other two arguments get involved in it (no big surprise there and DUH).

In most things in human life, nature, nurture, indoctrination, disease, nutrition and education, interact in complex ways, to make people what they are. Thinking that any aspect of the human condition from gender, to politics or whether you are religious or sceptical, is determined by one of a simple duality of either genetics or culture, is buying into a vastly oversimplified picture. The two sides of which are usually, as with all oversimplifications, promoted by people with political and religious agendas.

Physical biological sex is assigned as a convenience at birth according to genitalia.
Sexual identity develops naturally a little later it and would seem as hetero and Homo sexual trait appear at a very young age.
Gender identity similarly becomes more marked and developed with the onset of puberty though often appears years before.
Subtle personal sexual/gender preferences (personal turn ons, fetishes etc) seem to come in to play as personality develops in the same way we decide which tastes we prefer and colours we like.

Just an opinion based on personal observation.

All that aside it is no one else's business how an individual decides to identify or how they feel happy living their lives so long as it is not actively and directly hurting anyone else

I was born in 1959 and my family was poor white trash, military, violent and religious.
There were as many Trans people then as now, but we were coerced into silence and conformity, because our lives depended on it. I was ALWAYS aware at one level or another that I wanted to grow up female, after all they had so many more fashion choices. I told my grandmother when I was four years old and she told Dad and I suffered humiliations endlessly until my father died in 2001 by which time I was married and had two daughters.
I had spent my youth trying to fit in as a male hilariously overcompensating, even riding a Harley and wearing leather for about five years after my tour of military service. I exercised way too much and none of it was aerobic because aerobics don't make your muscles swell like a male kangaroo in rut season.
In the Navy I actually dated couples several times and ultimately received an honorable discharge for "homosexual" activity, but I never identified as homosexual or bi for that matter.
I flushed my DD-214 and made an almost lethal attempt at suicide in 1983. I married a Bulgarian woman in 1993 who was about as emotional as a Vulcan from Star Trek and had two daughters. My wife divorced me in 2007 and I went off trying to find myself but it would not be until 2016 that I embraced the truth and remembered all those nights as a young teenager where I prayed that God would help me, just let me wake up as a female. I hadn't wanted to face it but I had always been Trans, just repressed or oppressed into being dishonest with myself.
Three years went by before I told family and work, so yes I am out. The response broke my heart because everyone at least acted like they accepted me, it wasn't the huge disgrace that I had been programmed to believe, the universal abandonment would not happen after all.
Sadly my transition plans have been interrupted by the pandemic and I had a heart attack last year revealing my heart disease. So it's probable that I'll never complete my transition.

As for your question, I was born this way. It's not about sex it's about gender. I lost interest in sex a long time ago. Sex is complicated and based in trust and I spent an entire lifetime not trusting anyone for obvious reasons.
How much do you know about a person when the only thing you know is their gender? "Male", "Female", "Trans" tell you nothing at all about the person beyond absurd assumptions. I know Trans people that are conservative Christians while I'm a progressive atheist.
In short we are our nature, let people be who they are, don't expect special treatment for being who you are but by all means be yourself.
I'm grateful for every opportunity I get to bring my body and my psychology into harmony, if you're like me I encourage you to do something about it while you're young and strong enough to be happy.
I'd explain my gender dysphoria if I understood it enough to explain it to myself, but it has always been there.

Gee, I thought that with eleven comments surely someone would know more than the TINY LITTLE BIT I know AS TO HUMANS.
0 ) For a brief time after fertilization every fetus is female
1 ) Soon after fertilization, a “signal” results in the female genitalia re-forming as male genitalia, ovaries becoming testes, clitoris becoming penis, etc.
2 ) It’s now THOUGHT that a few weeks after fertilization another “signal” results in the female brain re-forming as a male brain.
3 ) when those two “signals” don’t match, gender dysphoria results.
4 ) Intersex is something else.

For better info, in PM on weekdays phone SF Sex, Gender & Relationships Info hotline at 1-415-989-7374.

People tell me god does not make mistakes. How about a 2 headed calf? On the other hand, it's hard for me to imagine a girl with a penis. It's also hard for me to imagine people fighting gender assignment problems at age 5.

I suppose, medically speaking, we are born with the genitalia ( the outwardly visible sex organs that is) that depict our birth Gender.
However, it is not until the early second trimester that the gender defining hormones begin to take effect, before then there IS No definable gender for a fetus/developing baby.
Post-partum ( after being born) the environmental, etc, influences do come into play to some extent but, more than likely, it is the production of hormones at the onset of puberty that can and do wield some influences over the future sexuality/sexual preferences, etc, of the person.
In females there is an ample production of hormones such as Estrogen and Progesterone with small.minute amounts of Testosterone being produced as well from time to time.
In males, there is, under 'normal' body circumstances, a constant supply of Testosterone being produced by the Testes and sent around the body, however in both male and females case there are exceptions where the Hormone factories get a bit over-excited/lax and those supplies are either either over-supplied or under-supplied.
It may worth remembering that MALE Testes were once EXACTLY the same as Female Ovaries, they were found up in the pelvic vault, and until Testosterone was released they had every chance of remaining there and becoming Ovaries.

People can be whoever they want to be, but if one is born with a penis, I will forever refer to them as male. If they are born with a vagina, I will always refer to them as female.

I can't say I truly understand, but that's okay. Understanding is far less important than accepting people for who they are. I don't need to put someone in a box or slap labels on them. I may never truly understand what someone is going through or how they feel about themselves and their identity but I'll do my best to accept them as they are.

I'm old-fashioned. I don't get the whole gender dysphoria thing. I guess live and let live.

As a Transwoman all I can say is "Baby I was born this way"... It wasn't easy to accept myself, I hid in my armoire for 26 years..I was a pleasant "man" to know, the interior me was a different story. As a bestie Gf put it when she met Me for the first time, " I never realized how unhappy you were back then"
She loves Me, for Who I am, even more now.
So imo it's all about social conditioning

Science has answered this query. I do not remember exactly what trimester in the embryonic development it occurs but at some point way prior to birth the fetus is flooded with hormones, there is some signal that occurs and depending on how much of one or the other the fetus gets this will determine the "sex" of the individual. This is the reasons that trying to assign gender once the child is born can be risky. What is hanging off the front may not match the xy chromosomes or is there is evidence of both genders (as does happen).
Culture plays a role in how we get raised and what boys or girls get to do. Always seemed like so much bull shit to me.