Glad to be of service.

I have one more comment regarding this part of the OP:

Gender identity is a psychological thing. Trans people say they identify as the opposite sex. Nonbinary people say they identify as neither boy/man nor girl/woman. Genderfluid people say they identify as both girl/woman and boy/man, one day they feel like a man and the other they feel like a woman.

Yeah, gender identity surely is a "psychological thing." So is OCD, clinical depression, psychosis and narcissistic personality disorder. All humans have psyches, but we do not all have the same psychological issues or mental illnesses. Not everyone has OCD, depression, psychosis, personality disorders. Saying this doesn't delegitimize the experience of those who do have these problems.

You and the genderists are essentially saying that because a certain small segment of the population has a particular psychological problem, it means every human being on earth must have the same exact problem too - and anyone who won't go along with this is "invalidating" the identity and experience of the people who do have the problem. Which is like saying because some people are diabetic, everyone else must be too - and it's somehow mean and offensive for the rest of us not to constantly check our own blood sugar and inject insulin to show our allyship with, and inclusion of, diabetic people.

There is no such thing as feeling like a man or a woman, boy or girl. We all are either male or female. It's a matter of material, empirical fact, of verifiable reality.

These groups of people feel like they are in the wrong body, and are desperate to get out of it, to change their body to look like the body they want, a man who identifies as a woman gets hormones because they are desperate, they hate that they don't have boobs, vagina, etc and they get surgery too, they feel they are in the wrong body.

This is hogwash. Most trans lobby groups and TRAs are now running away at warp speed from the notion that being trans means feeling like you're in the wrong body. They're even claiming they never said anything about being in the wrong body in the first place - or if they did say it, they didn't really mean it.

Contrary to what you claim, most males who identify as/claim to be women are not "desperate" and full of hatred for their male bodies. They like their dicks and balls just fine. Which is why nearly ALL of them keep them. Many proudly display their male genitals all over social media, and threaten to rape and choke women with their "lady dicks" too. Blaire White, Gigi Gorgeous, Munroe Bergdorf and zillions more "transwomen" all have their dicks and balls and are definitely NOT "desperate" to lose them. Ever.

For males who claim to have an opposite sex "gender identity," the motivation is always sexual. These guys are erotically aroused and enraptured by the idea of themselves as females, and by the idea of being desired and lusted after as if they were females coz they think being seen as a fuck toy is the highest compliment and the greatest pleasure. They want to be sexually objectified the way they themselves sexually objectify girls and women.

The clinical criteria for "gender dysphoria" (previously "gender identity disorder") in the DSM shows that having an opposite sex "gender identity" is all about wanting and preferring the sex-stereotyped clothing and grooming, mannerisms and (some of the more obvious) social roles and interests associated with the opposite sex. It's all about enviously desiring, pining for, and coveting "the goodies" the person perceives as belonging to the other sex.

(I say "some of the more obvious social roles and interests" here coz males who want to be girls/women always want the pretty and fun stuff, like the dresses, frills, makeup, big round boobs and being asked out on dates. They seem far less interested in other common social and physical aspects of femaleness like being forced to veil or dress modestly, being banished to menstrual huts, getting piles and stretch marks from pregnancy, the agony of childbirth, suffering from breast cancer and gynecological diseases and conditions, going through menopause, not being allowed to eat until the males in the family have had their fill, or a lifetime spent cooking, cleaning, caretaking and being made to put everyone else's interests before their own.)

The whole theory of "gender identity" has been pushed on the world by males to cover up what motivates males to claim they are trans. The vast majority of males who ID as trans are attracted to females sexually and have a paraphilia known as autogynephilia. A minority of males who ID as trans are attracted to males sexually, but they only want to bed straight males; for these guys, the driver is internalized homophobia and a usually a highly fetishized view of femaleness that also smacks of AGP.

Another common characteristic of males who identify as trans is narcissism.

https://4thwavenow.com/2017/12/07/gender-dysphoria-is-not-one-thing/

https://thecritic.co.uk/issues/january-2020/sissy-porn-and-trans-dirty-laundry/

https://www.them.us/story/tumblr-adult-content