In that case wouldn't everyone have a gender identity
I think they do, especially if it means "do you think of yourself as a man or woman"
We can think of ourselves as men or women without relying on any "internal sense" to reach that point, but most every definition of gender identity is explicitly grounded in subjectivity of experience. If we use the same process (reasoning from observation) to detect sex in ourselves as we do on random passerby at the beach then we are missing an essential element of what people mean when they talk about gender identity.
Perhaps, though, you didn't mean "man or woman" as sex categories but rather something else such as social roles? Worth exploring, if so.
That your internal behaviours are the same as most people and therefore can be used to generalise from.
I do not recall asserting any such belief in that thread; seems to me you must be reading it in between the lines.
OP was about three people (Thrace, Wintemute, & Coleman) who seem
not to be able to generalize from their own subjective experience to the broadly held notion that everyone experiences gender identity. I find those people fairly lucid and even relatable, but even if I made the same assertions which they do, that would not constitute an attempt to generalize but rather an attempt to exceptionalize.
I came to the conclusion some time ago that it's okay for me to not be able to personally feel what other people feel. I will never be able to feel the unpleasantness of menstruation because I don't have a uterus or the hormones that usually accompany it. Similarly, I will never be able to feel the gender dysphoria that trans and nonbinary people feel. That means that I don't have the right to judge or make assumptions about the way other people are feeling.
That thread was designedly not about what "trans and nonbinary people feel" but about the claim that
everyone experiences gender identity, including people—such as ourselves—who do not experience any discomfort when considering our primary and secondary sex characteristics. The degeneration of the discussion into focusing on transgender and nonbinary identities was perhaps inevitable, despite clearly warning against it in the OP. The question remains whether
gender identity can be conceptually nailed down in such a way that basically everyone who takes the time to really think about it would eventually nod and say, "Aye, I've got that."
Analogies are invariably imperfect, but consider the idea of consciousness. We can imagine p-zombies
WP who lack it, but everyone we talk to about consciousness affirms that they experience it and we tend to take them at their word, even though the concept itself is pretty hard to nail down. If I were to run a poll about whether every adult has the property of consciousness, we'd generally agree that they do, after setting aside coma patients. It would be quite difficult to find serious writers like Wintemute and Coleman asserting that they have done a bit of introspection and yet find themselves to be unconscious.