1.Every culture have some sort of idea what is a man or a woman, if someone argues "X culture AND Y culture believe in the third gender and therefore, there IS or MUST exist a third gender.", argue back by asking about the inherit flaw of those two cultures and if THEY THINK that makes those the cultures right? They're trying to use old cultures as some authority on subjects because they're simply old and they're trying to use the existence of the concept of "differing cultures coming across the same concept therefore, said concept exists" as an argument, ignoring the blatant fact that no ideas are as unique as they seem. To make an analogy: Humans in different lands have figured out how to make a net using by drying and weaving fibrous plants from their respective environments, so they're going to differ slightly in uses (e.g. catching fish, catching land animals), but at the very basic of the concept of a catching/trapping equipment woven from fibrous plant material, they are still all "nets.”

2. Different cultures make things up all of the time, it still doesn't change statistics (e.g. domestic violence, employment), until morons decide to group transwomen into statistics concerning the victimisation of women. Example of dialogue:

Trans: Indians believe in a third gender and they call them "hijra" and Native Americans have something called "2 spirit", therefore there is a third gender!"

Me: India also have hundreds of gods, believe that women should stay in the kitchen and I'm really a rabbit, trapped in a spirit of a tiger who secretly wants to be a goat, trapped in the human body, so I have three spirits (human, tiger, rabbit) because I know I could never be a goat so that makes me a three spirit. What's the difference between my belief and theirs? Just remember that 99% of the human race have either XX or XY chromosomes, have a standard structure of a reproductive system, the question is, how much should we kowtow to the ideology and WHY should we?

Anyway the problem is the subject on gender is so diverse that's hard to nail down a proper argument on the spot. Consider, are they arguing using science, culture, psychological (maybe a few other things)? Find a solid foundation in some of those areas. Here’s a few examples:

Culture: People make things up all of the time and create an effective systems to stabilise their own society, gender comes into play when it comes to how one contributes to their own society (e.g.who fights in war, how we raise our kids in relation to how society treats them).

To clarify my example "how we raise our kids in relation to how society treats them", in some countries having a vagina or a phallus determines your role and expectations in their society, parents in those societies have to raise their children in those roles to maximise their survival rate in their society (e.g. telling girls to cover their skin for whatever reason related to safety and religion).

Psychological: Some people have anxiety, some people have depression, others have schizophrenia, but we don't try to validate their image of themselves or their self worth, we try to support them in a way that helps them. They think they're born in the wrong body and are happy being the opposite sex and are not satisfied with simply looking like the opposite sex and it seems a lot of the outspoken groups of society are happy to concede with their delusion spawned from their insecurity (probably caused by their environment making them focus on gender and actually putting in a “psychological reward” if they come out as some sort of minority or maybe they just really like).

Science: None of the research is conclusive and some of them are worded in a way as if there is an actual “male brain” and “female brain”, based off the research I’ve read, there’s a brain structure that is shown typically in females and another brain structure shown typically in males (key word “typically”), it just means the subjects of the test use those specific areas of the brain a lot more and their brain structure could be like that for various reasons (maybe the trans subjects were just actively encouraged to participate in activities which use those areas of their brain? Maybe they were just born with it?), it doesn’t mean they were born in the wrong body. Also most research samples which I’ve seen written is pretty small, involve only adults and does not factor in the subjects development of the brain from age 0 to the time they conduct their brain scans, which is important because research also shows that the human brain is continuously changing as the person experiences different things.

Sociology: There are intersex people who have both female and male reproductive organs (whether both sets of organs work or not or are probably developed would be related to a different conversation) or have and extra X-chromosome and because of this, people think that it means there’s something “inbetween” when it comes to gender identity and therefore there needs to be a special way to address intersex people and use this in their arguments about the legitimacy of being trans, however people don’t seem to realise to facilitate effective communication, a parent just decide to use the standard “he” or “she” for their kid, because they can only see what is external of the child and not much is known about their anatomy until they hit puberty. However does this mean intersex people are trans? No because “trans” means “transitioning” ,does this mean gender identity is a real thing? No, because it’s really a generalised descriptor of what we based off what we are in relation to people around us, we’re all just people with feminine or masculine characteristics/behaviours that doesn’t really determine what sex we are.

I personally think people should be addressed based off their phenotype (physical characteristics which they’re born with) as we can’t simply going around asking what their pronouns are or look for pronoun badges when we’re trying to figure out how to save their lives in the ICU (and people in general should not be ticked off when they’re being misgendered and if they look like another gender). We’re all programmed to address each other by specific pronouns by how we look at the person. (Yeah I’m saying this even though it’s not relevant because there have been cases where stupid teenage girls acting shy talking about their period pain to busy doctors when they’re calling themselves “male”).

Edit: On second thought, addressing people by their chromosomes would be better, anyone with only Xs are female and anyone with a Y is a male.