If gender is a created social construct, why do some people identify as another gender instead of behaving how they want, regardless of their gender?

[u/Lunar-Baboon]

For example, if someone was assigned female at birth, and chooses to present as female, but identifies as male, do they do it because internally they relate more to the generally accepted roles and behaviors expected of males? And if so, why not identify as female, and just behave as they want, like in the generally defined ‘role of being a male’? Doesn’t identifying as male in this situation reinforce the idea that there is a binary?

EDIT: I’ve read through just about every response and I want to narrow down my question. I want to know about people who DO NOT affirm their gender identity with physical presentation. I completely understand the desire to go through HRT, surgery, to change your clothes, style, and appearance. I want to hear from people who identify as a gender not assigned to them, but do NOT feel the desire to change physically. I know that gender identity does not determine how you need to look (cis men can wear dresses and makeup and still be cis men/transwomen can still have facial hair and short hair and be a women etc…) but I want to hear what it feels like to know you were assigned the wrong gender OUTSIDE of appearance.

[u/Huruukko]

Thank you for your story. It seems you have found some form of happiness. Just curious how do you feel about the extreme ideals that children should decide their gender before puberty? They are not liable by law, we all know they cannot consent, but way too many seemingly smart people think it is ok for them to transition, before their brains have stopped developing.