I can only tell you how I see it.
Like most parents, mine gave me a name when I was born. (Let's say it was "Larry".) And although I can't say as I ever really hated the name, I also never felt right with it. I can't tell you what's wrong with the name Larry. I've met others with the same name, and the name seemed fine there. But Larry just didn't..."fit" me. I never felt like a "Larry", if that makes any sense. During high school, I picked up a nickname among a few people. ("Lex".) And I really liked it. Far better than I liked my "real" name. So I tried to encourage people to start calling me "Lex" instead of "Larry".
When I got to college, I was more or less starting with a blank slate. And so I decided to just introduce myself as "Lex". So everybody in college called me that. A few learned my real name under one circumstance or another....and, to my surprise, most immediately seemed to intuit what I did. "Larry?! You're not a 'Larry'. No way. You're Lex." They didn't just find it surprising that I went by a name that wasn't my birth name - they found, once they got used to me as "Lex", that they didn't feel I was a "Larry", either.
A very few people are kind of jerks about it. Some people seem to delight in trying to figure out what my birth name was...and, if they find out, telling as many people as they can what that birth name is. "I call him Larry because that's his REAL name. LARRY. It's not Lex - it's LARRY." And of course, they can claim that they're not being jerks at all - they're simply being REAL. They're calling me the name my parents gave me. Isn't Larry my name? Why should they not call me that? But, come on - they're being dicks.
As I started to get to know a few trans folk, this whole thing is what kept popping up in my brain. The idea that something wasn't exactly right surrounding "who I technically was" and "who I felt I really was". The long time it took me to sort of come to grips with the idea, and the attempts to get people to "accept" this new aspect of myself. And the people who fight back against it, often with claims of "I'm just being real about who you really are". Obviously, feeling you don't have the right name is far easier to deal with than feeling you weren't born the correct gender. But I sense some vague parallels there.
I can't explain why I'm not a "Larry"...other than to say with great certainty that I'm definitely not a "Larry".
And because of that, when somebody says that they're trans, or gender fluid, or whatever else....I usually believe them. Do I think they're all correct? No, of course not. But if somebody wants me to call them male or female or both or neither, I haven't found any problem with that.
Lex