[Serious] Please convince me gender is binary

[tackattack]

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There has been a lot of discussion on it lately, and there's a lot of informed and actual people that struggle with gender. Perhaps I need an education in gender identity, But I only see gender as binary. I'm open to be convinced otherwise. Let me start with a statement, which I'm sure people will jump all over.

I define gender normalcy as that which functions according to its design. Our design is in our DNA as male or female.  Gender identity uses the same words and is thus binary. Is this a true statement? Elucidate me.

PS- I don't think I did the serious tag right, I need an education on that too please

I am a transgender female; some of my earliest memories were of wearing make-up, my mom's dresses/skirts, daydreaming of getting married, carrying a baby within me, etc.  (But, of course, I am a biological male.)  And, so, what's the big deal?  What do you and yours expect of me?

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If by me and mine you mean white males in their 40's idk and dgaf, for me personally:
There isn't a big deal unless you're making it a big deal. I personally don't think societies general views and classifications supercede my own personal definitions and beliefs. If you walked into a men's room I was using, I'd nod, say hi and see if you washed your hands after (the same as I do of every other person who walks in). Now if you walk in, look around and seem shocked that you walked into a men's room, I'd assume you were a female who walked into the men's room and ask if the women's room line was too long, like I would do for any woman walking into a men's room. As for expectations, I expect you to be confident in yourself and your identity individually. Socially I expect you to conform to legal norms and classifications (ie. Using the male urinal to stand up and pee, going to the men's changing room with your dresses and skirts, etc) that you yourself accept by ackowledging that you are biologically male.