I don't know if it's 'cause I'm a closed-minded twat but I don't get how you can fluctuate between genders or even have none. I never felt the need to distinguish between my gender and my sex. I refer to myself as a "man" because I have a penis, and the line of thought kinds of stops there. I might not be a very good man because I'm fully aware I fail at my gender role but that doesn't mean I'm not one.
Not gonna say anymore on the matter lest I step on a mine and blow up. This subject is an incredibly finicky one.
My train of thought on the subject also pretty much begins and ends at having a penis, thus making me a man.
I don't really care about traditional gender roles either, as they aren't truly relevant to the modern world.
You both are absolutely correct that having a penis or lack of essentially is what distinguishes between a man and a woman in the physical sense, unless you go into hermaphrodites/intersex people that have both genetalia.
However, mentally is a completely different monster compared to physical. One can have all of the physical characteristics of a man, but believe strongly with all of their heart and soul that they're actually a woman. Physically still they're a man, but mentally they're a woman. They think like a woman, act like a woman, their inner voice is most likely a woman, and they like to do things that women normally enjoy (which in itself is another topic I'll talk about in a sec), but that the physical part of them is still completely male. That's why crossdressing and potentially going beyond that is such a common thing these days.
For some people, drag is a performance thing where they play a character. For others, it's an experiement to see how it feels to "be" the other sex. And for some, it's the comfortable transition they can take until they're ready/able to go through the more grueling part of becoming the other sex. For the last one, it's essentially stepping out of it being "drag" and into the beginning stages of becoming transgender in the physical sense (as at this point they'd already be so in the mental/emotional sense).
But considering we do have transgender people on here, perhaps they can say it better than I can.
Anyways...moving on beyond that, considering it's highly possible for people to feel as if they're in the wrong sex (and again, it's actually pretty common), it's just as possible for someone to feel like they neither want to be masculine or feminine. They may be a man that enjoys watching football, playing Call of Duty, hunting, and other things that would attributed to "masculinity," but at the same time they might enjoy shopping, baking, watching ballet, getting a pedicure/manicure, and other things that may be attributed to "Femininity."
In other words, they adhere to neither term in the mental/emotional sense, but they jump around the spectrum because they believe that both sides have absolutely no real meaning and shouldn't "define" people by who they are.
Some will go further than that aspect and go into guys wearing dresses, heels, and/or makeup, and likewise women wearing clothes that may be considered more masculine, simply because they want to.
I don't really consider myself "Gender fluid" (I do like defining myself as on the border between masculine/feminine, but with one foot more in the masculine side) but I do agree with the reasoning of people that do. It should be more about who you are and what you like, rather than trying to see how masculine/feminine you can describe yourself as because you like so many manly/girly things. If a guy wants to wear a dress, why shouldn't he be allowed to without having to look like a woman to do it?