Sunburnt - re "We are all born with a gender identity"
Speak for yourself. I am no different than a man, except physically, and never have been.
"But if someone repeatedly says "he" and "him" to me I take offence. Why?"
No idea. Why do you?
If someone were to repeatedly say "he" while referring to me, I would think he is a bit blind or has some sort of cognitive problem.
"I know I'm a woman. And if someone tells me I look like a man, it stings. I get a jarring feeling. I take offence. I feel insulted."
Because you think it means you are ugly? Sorry, I really don't get it 
"Try some empathy. Thats a scratch on the tip of the iceberg of what gender dysphoria feels like. Imagine walking around every day with that feeling as a kid in school and the fear of what might happen to you if you tell someone..."
If one day I find myself convinced that I am something that my eyes say I am obviously not (man, alien, lizard, cat, a toddler, etc), ridicule & ostracisation would be the least of my worries. I would be terrified that I have had a psychotic break.