I want to reiterate that it's good to want to learn and educate yourself, and expand your understanding of the world! Totally happy to talk about this. I think others have done a good job covering this but I'll throw in my perspective too.
I'd assume this person to be speaking lightheartedly or to mean it like "here's a new gender you may not have heard about". When people come up with new words for how they identify, it doesn't mean they're inventing new concepts - they're just finding specific language to describe what they feel and who they are. Not everyone feels the need to narrow down what they feel that much or use microlabels, for many people existing words work just fine, and others don't even feel the need to call themselves anything specific at all.
I myself am bigender; I'm both a man and a woman at the same time. It took me some time to figure this out and I thought I might be other things along the way, and it's entirely possible that my understanding of myself will shift or that someone will introduce me to something that encapsulates my feelings even better. For now, I am confident in who I am and the language I use to communicate that: I'm nonbinary, more specifically bigender, and I use both he and she pronouns.
It's a common experience to not have anyone you know to talk to about certain things or be intimidated in such a situation! I've been there myself, and it took some time to learn, but it's absolutely possible.
I'm not Christian myself, but I am spiritual and was raised LDS. A way I often find useful to look at it is that, when creating people or sending them down to Earth, God sent some souls to bodies that don't fit them quite right. For some that's literal and physical, for others it's due to the expectations of the majority of society, and often both. This is part of those individuals' trials on Earth; both the oppression they face and their journey to become more personally comfortable, whether through social transition or medical transition (because medical transition is just a type of healthcare).
Because I believe in a benevolent God or Gods, I also believe that that God is not and cannot be homophobic or transphobic. God encourages love and being your best and happiest self.
Expanding on this - yes! It's important to note the different things that cause people to realize or act on the fact that they're trans. For some people, it's an internal feeling, a fact about yourself that you can just know. Sometimes it takes people a while to realize it, and it's hard to explain, but it's just there.
Another aspect is the wanting to present and be perceived as a gender differently from the one assumed at birth, because you find that that makes you happier (gender euphoria) or decreases your discomfort (dysphoria), and so you identify as the gender you wish to be (and are, you just don't feel it in your soul, whatever that means). Social performances of gender and its presentation are made up and can be easily contradicted by anyone, queer or not. Being transgender is more than that.
There's also physical gender dysphoria and euphoria. Some trans people don't feel this, and that doesn't make them any less trans; no one's experience is exactly the same. But many trans and nonbinary people do report physical discomfort and extreme distress over the bodies they were born into which can be alleviated with medical care.
Any of these things and most often a combination of them leads people to realize that they're not the gender people assumed from their genitals (which isn't even getting into intersex people; biological sex is not binary itself).
Tl;dr it's not simply wanting to do things society generally considers masculine or feminine; it's about your inner inherent feelings, whether of your own gender or of dysphoria or euphoria leading you to realize that gender. Trans men are men, trans women are women, and nonbinary people are people; the world just takes some extra time to realize it.