Hi, so you've been assigned female at birth, but your gender is non-binary. (yeah, first thing I want to tell you, if it can empower you a bit : you're not female if your gender isn't female. your gender has no relation at all with your sex caracteristics (sex is a cultural construction also) or the one that was assigned to you at birth.
So, that being said, you say you "want to choose one for personal reasons". You mean you would like to identify either male or female, so that your gender could be seen as a real one by your parents, is that it ?
Well, i can understand how it's important for you to have your parents support, and that they believe you and the reality of your gender.
My question is : if you're neither a girl or a boy, trying to identify like either one or the other, how will that feel for yourself ? Would you be ok with that ?
Gender isn't something you can choose. So I'm not sure what are your needs here.
For instance, if you feel the need to modify your body (like by taking hormons, having some surgeries etc), then it can be strategic, in order to obtain that, to say that you're a boy (even if you're not), if the obtention or such medical things depend on psychiatrists who don't recognize the reality of non-binary genders.
But in the long term, it may not work out like you want. In particular with your parents...
Your life is yours and yours only, not your theirs. Would you be ok with being seen/considered by people as a boy if you're not one ? Or as a girl, if you're not one either ? Since non-binary is generally not considered officially, would you be more comfortable being socially seen (most of the time at least) as a woman or as a man ? Are you feeling any dysphoria at all (socially, physically etc) ? What's the most important to you ? Fitting your parents' illusion about the gender of their child ? Living your gender as it is and maybe educate your parents about non-binarity (I mean, lots of countries in the world recognize their existence, either socially and/or legally..) ?
I'm not saying there are right or wrong answers, right ? To each their own priorities, and it's clearly your decision in the end, since it's your life. You'll do what's best for you.
I guess that are just some questions you can ask yourself to be sure you'll have thought things through before taking your decision :)
You can also test how you feel when you're perceived as a man, to see how different you feel, if it makes you feel better than when you're read as a girl, or is it in fact even more uncomfortable ?
Feel free to reach to me if you want to dig deeper into what your needs are. I'm a trans activist for a long time now, and I've been a listener (irl) for trans people or people in questionning, so I'm here if you need to talk, see ya!