It's a false equivalence, and a complete misunderstanding of biology, and the sociological impact.
Appeals to authority can be a fallacy, except in the cases where the authority is actually talking about something in their area of expertise and those authorities have achieved consensus. That being said literally every major, reputable, medical association in the entire world agrees that transgender people are who they say they are. And literally zero of them think that trans race, trans age, trans career, trans species, etc... are valid things...
Next up let's talk about biology.
It's very common for this kind of person to think that male and female humans are as different as humans and attack helicopters. They believe that trans people are just cosmetically their gender and "biologically" whatever their birth sex was underneath.
The biological reality is that male and female humans are not only similar, every single human has genetic code for both masculine and feminine features. Chromosomes pretty much stop mattering after the gonads are formed. And every single human produces chemicals that are capable of activating masculine or feminine features - naturally.
These sexual differences are pretty much 100% influenced by hormones that naturally occur in every normally functioning human body.
Estrogen activates the feminine features, testosterone activates the masculine features, and both chemicals occur naturally in all humans, and both masc and femme features are activated in different amounts in every human. Most the most part, human sexual organs start out as the same parts, and diverge based on hormones - not chromosomes. The clitoris and penis are actually the same organ and only diverge due to hormone exposure. There are birth defects where the urethra doesn't move or moves too much. Trans men who take testosterone can see a clitoris grow significantly. All of this is experimentally testable.
A penis doesn't form as a penis because those cells between someone's legs have XY chromosomes. Those cells are generic, they were exposed to testosterone and that turned them into a penis and scrotum - if left alone they would have been a clitoris and vagina.
It's very clear that trans people are "born that way" - Trans people who experience dysphoria can change their bodies, and make that dysphoria go away - nothing else works. We don't have the technology to fully understand how the brain works, so we don't know what the specific cause is. One theory is that trans people had a hormone imbalance at some critical point in development that altered their brains to expect different biological features, not having those things causes distress.
so what about race
Race can be boiled down to two things, your family tree and the culture you were raised in. If you are part of a race, then one or two of those things are true, you are part of the family tree or you were raised in that family's culture - and probably both.
Your race can even change based on public opinion of this 'family tree'.
To be clear here, this is public opinion of your family tree as a whole, not of a specific individual - a white-passing black person is still a black person.
Are Irish people "white people" in the US? Yes, but they didn't used to be! There are racial slurs to refer to them (ever heard of a paddy wagon? how about the Irish drunkard stereotype?), they were discriminated against, there were loads of negative stereotypes. Absolutely nothing changed about Irish people to make them white other than public opinion. Irish-American culture still exists, they have traditions and values, I don't know much about it other than being from Boston and seeing them from the sidelines.
Similar things happened with Italian people, there were slurs, and discrimination. Today they are essentially just white people with their own subculture.
What if me, a white woman with Scottish heritage said "I'm Italian American" - essentially I'm walking up to a group of people and saying "Hi, I am part of your family now!" So unless i'm adopted or married into this family by the members of that family, I'm doing something really inappropriate. If I start modifying my body to look more "Italian" (whatever that means) and wrapping myself in Italian stereotypes - that's super offensive.
If i went to Scotland, and found my ancestors, i could try to reclaim my heritage. Essentially, i'm the long lost cousin. I may or may not be accepted based on the opinions of other Scottish people. Personally, unless that happens I wouldn't call myself Scottish. But, I do have the family resemblance.
This is also why there's no such thing as "white culture" - there are hundreds of different cultures, but everyone who participates in these diverse subdivisions is considered to be white.
People who are transracial in the Rachel Dolezal sense are exceptionally rare, so rare as to be nonexistent. There is literally zero possibility that the desire to be transracial in her sense can be biological in origin - it's a physical impossibility. There's no way to time travel back to give you a different upbringing. There is no naturally occuring substance to rewrite your genetic code so that you were the child of different parents. These things cannot happen.
Transgender people on the other hand are raised in the same culture regardless of gender. You get to be raised right alongside your brother or sister, you aren't putting yourself into an inappropriate social space when it comes to culture. A white, upper middle class cis boy from upstate New York while know more about the cultural expectations his sister experiences culturally than he does about what it is like to grow up as a poor black boy from rural Alabama. Social differences between how people are treated and behavioral expectations based on what physical sex you are perceived to be exist, but are very individualized.
Age
If you went around the sun 23 times, that's an objective fact. We don't have time travel.
Species
Humans and cats share a common ancestor from millions of years ago, you don't have any "cat" genetic code in your body. So if you are claiming to be a cat, you are just someone who really likes cats - or maybe it's a pagan spiritual thing or something.
When it comes to xenogenders, my understanding is that someone who says they are cat-gender is simply using an analogy of cat behavior to their relationship with gender. They don't believe that they are actually physically supposed to be a cat.
Other nonsense
You have a doctorate or you don't, if you think you have a doctorate when you don't, you are mistaken, being a fraud, or delusional.
in conclusion
And that's what most people who use these arguments are: They think trans people are: mistaken, delusional, or frauds. That's what they mean when they say stuff like this. And they are absolutely wrong.
They always scream that trans people need therapy, even though this is one of the first things trans people start out doing.
When they say we should have therapy, they think we are delusional and should be convinced to accept that we are our assigned gender at birth - even though all the studies and science shows that trying to convince a trans person that they are their birth assigned sex is conversion therapy and makes the trans person worse off.
