There were some tweets from way before, someone saying 'other animals have no gender identity' so this trans right activist told her "other animals do have a gender identity, due to the lack of cognitive ability to identify as anything but their own sex, other animals can only identify as their own sex while humans can identify as something other than the sex assigned at birth"

Oh for goodness sake, how could they even prove that animals have a gender identity when you can't do it whit humans?

Sex is observed, not assigned, at birth. Nobody is born in the wrong body, you are your own body. If you want to say that is our brains what matter, well, your brain is still a part of your body and every cell of it is still either male or female. Sex is about reproduction. In anisogamic species like ours, individuals produce specialized cells with half the DNA (gametes) for reproduction purposes. Male individuals are the ones who produce small gametes (spermatozoon) and females are the ones who produce large gametes (ovum). Then, a spermatozoon and a ovum fuse to form the zygoto, restoring this way the normal amount of DNA. Some species are hermaphrodites, which means they can produce both male and female gametes. Humans are not hermaphrodites, though. There are several genes involved in sex determination in humans, but the golden star is the SRY gen. Basically, if this gen is present the embryo will develope as male, if not it will develop as female. As this gen is located in the Y chromosome, XX individuals are females and XY individuals are males. There are some people who have a disorder of sexual development (DSD), but they are rare and they are still either male or female, i.e. they don't produce a third type of gamete.