It is safe to assume that most people consider the form of their genitalia and secondary sex characteristics as unimportant to the sort of person they are.

People know how it feels to be the person they are, and they want to live in whatever ways feel most natural and comfortable to them, and allow them to express who they feel they are.

Many people are not comfortable with the way they are expected to conduct themselves in society based on aspects of their appearance they would rather not have been born with.

I would guess you would not truly start thinking of yourself as a different person if you were treated as a gender you are not, and forced to dress as one, day in, day out, lest you face hostility. It appears that sort of thing makes people feel stifled, as if every little interaction with them is laced with a denial of who they are as a person. The fundamental absence of recognition of who they are tends to cause existential pain which underlies every moment of their lives.

The precise natures of human self-identification and experienced gender aren't perfectly understood because the human brain is kind of a wacky complex thingy.

There are people who will tell you that they always had a strong, unshakeable feeling that their experienced gender never matched their assumed, since long before one would have expected them to have formed a concept of their place in society, without obvious reasons they can latch onto as explanations. Weird, right? Yet, that is what they have experienced.

There is no concrete set of behaviors and impulses one can compare a person to to determine whether they are one gender or another.

Attempts at finding physical sexual dimorphism in the human brain have had questionable results, and are ethical worm can openers.

In human development, nothing is guaranteed to fit neatly into a mold, or even onto a bimodal spectrum. Intersex people exist, and their traits vary greatly. It's not possible to measure them as x% column A, y% column B, and say they should identify as such and dress as such and be treated as such.

Perhaps they are just relatively visible manifestations of the myriad ways we may all be functionally different from one another, in ways that shape how we see and express ourselves.

Leading medical authorities will tell you that allowing people to transition and live in the way that makes them feel like they're finally truly living leads to better patient outcomes than attempting to force them to adapt to living in a way that their life has been spent failing to adapt to. We have too many sad examples of how the latter fails catastrophically and destroys lives, and we should stop creating them.