I can only provide so much information and can't speak directly for anyone, but I can answer some of your questions from a broader perspective and give you some links you may find useful or interesting.
also I don't mean to be a dick but why do people have to claim to be non gender binary?
The most important thing to remember is that the main point here is people trying to be the most authentic version of themselves possible, often at the cost of significant physical and mental strain, on themselves and on their relationships with people who, intentionally or not, see them differently and hold them at arm's length because of it. People don't do that because they just want
to. Very often, people will see LGBTQ issues, and because it doesn't fit within their definition of normal, it must therefore be inauthentic and somehow and attempt to trick them or something.
I like Survivor, and this issue came up recently with a contestant on the show. His name is Zeke, he was on a whole season where nobody knew he was female-to-male trans. He didn't say anything, nobody knew until some people dug through his history online and found his college application form, which had him as female. This season, he came back and still told nobody, until another contestant outed him and tried to use the fact that he was trans and nobody knew against him. He wrote this column about his experience with coming out, the process for him, and being outed in such a public forum. As an actual trans person, his words should have a bit more weight here than mine:http://www.hollywoodreporter.com/live-feed/survivor-zeke-smith-outed-as-transgender-guest-column-991514
I'll try to add a bit more information where I can.
There's also a distinction between sex and gender, and being gender non-binary is kinda separate from trans. Masculinity and femininity are not the same as your sex; it is, to a large degree, socially created. The "gender binary" is an idea that gender, sex, and sexuality are all connected. So, a person born male, they will have a certain masculine appearance, act a certain way, and be attracted to women, and vice versa. Non-binary gender is the refutation to that idea. To the extent that you can say a feature is "biologically masculine" or feminine, there's still a certain amount of people who are going to have or not have that characteristic (in personality, in outfit, etc), independent of sex. Non-binary gender sort rejects the idea that it's this male to female spectrum, and that there's far more other factors, though it also doesn't mean people aren't allowed to subscribe to those binaries if they want- just don't force them onto others. Being non-binary can be as simple as ignoring those social norms. One day, a person may identify in a more masculine way, and dress a certain way, act a certain way, etc. Another they may identity and act as more feminine and dress in a way that might be considered more feminine (like wearing a dress, makeup, whatever). Some people with male sex organs identity as female in terms of gender (again, this is separate from their junk) expression.
This is a good, quick link about non-binary gender, even though I'm not a huge fan of the whole top 10 format thing:http://everydayfeminism.com/2014/12/myths-non-binary-people/
There's also the idea of gender roles- men are the providers, head of the family, etc. It's become more and more acceptable to throw out certain parts of this binary for a long time, but to a large extent the system still remains, and each step usually has significant traditionalist opposition.
The wikipedia article actually covers this pretty well, too:https://en.wikipedia.org/wiki/Gender_binary
I mean not to be a dick but aren't their only two genders(male and female) and If you denied that you are either then you denied the existence of Sexual intercourse?
We've already covered the difference between sex and gender, so we'll just talk about sex here. First, saying there are not only two sexes does not deny the existence of sexual intercourse. Yes, we do have the two standard sets of genitals that interact in a specific way, but there's even people who don't fit into either category with that, called intersex. Being a hermaphrodite would fall into this group, but that's a very outdated and overly-simple example- there are people who, at birth, have basically any imaginable combination of genitals, chromosomes, or any other indicator for sex that you can think of. Some people who may develop as a "typical" male or female in terms of their body can, upon genetic testing, turn out to have chromosome combinations that would typically be considered the opposite sex and would never have known it without genetic testing.
So, if even something which seems as clear-cut on the surface as the physical development can have such variation, you can see the extension on psychological development, how even if we were to say gender identity (which is, again, not the same as sex) were entirely biologically determined (and it isn't), the factors there can be significantly varied, far more so than even sex.
In my religion (catholic) they say that God created two genders for a reason(to mate)
And this is the crux of the issue to a lot of people. While you are, of course, free to have your religious views, keep in mind that not everyone subscribes to that. What ends up being a typical description
in nature, that things typically are a certain way because that is what the multiple, messy natural processes that make us who were are resulted in, often turns into a hard and fast rule in religious dogma that doesn't match the reality of the situation. The resulting thinking from this is that anything which does not match the typical or mandated "way things ought to be" must be wrong, and anyone who doesn't match it must be trying to trick you. I'm sure you've heard the common tired trope of how homosexuals, rather than just wanting to live their lives, have some sort of agenda beyond that and want to turn everyone's kids gay.
This gets a little bit separate, but to your point specifically that god created two sexes, tied to the concept of gender, and one individual is one thing and that's it, looking within nature, you see that what we'd think of as typical human sexual dimorphism (two separate sexes with separate sexual characteristics) isn't the only game in town. Even in species that do use that kind of system, the mechanism is different. Humans use the XY sex determination system, where each parent contributes a chromosome to the pair, and people with XX are female, XY are male, as determined by what's donated by the sperm, since the only place to get a Y chromosome is the male (though keep in mind still, while it's very rare, you can end up with XX males or XY females, as I mentioned earlier). Other animal groups may use something different- birds typically use something called the ZW system, X0 for a lot of insects- similar, but based on a slightly different mechanism. Some fish and reptiles have their sex determined by temperature during development. Some species have/use male or female sexual characteristics and genitalia based on their position within a hierarchy in a group, or what they need to use at a time. So, the idea that male/female sex being tied to one thing is a strict natural order with no fluctuation or differences isn't true. The point is, the fact that there are typically two specific types of genitalia used for mating doesn't really have any additional implications for the individual carrying them.