It's quite informative to read the forums where trans-identifying people discuss this, to see how these false beliefs develop. One can observe the trajectory of, say, a male who wants to be a woman. He'll start out with desire to be a woman, move onto the idea that he "feels like a woman" despite having no insight whatsoever into what being embodied as female is actually like, and then slowly, within the echo chamber of like-minded males, he'll start to believe he actually is a woman.

Sometimes this will be through believing he has a "female brain" in a male body. Or perhaps he might think he's "born in the wrong body". Or maybe he'll start to believe that being a woman or a man is based on some internal "gender identity" of which he has the female type. Sometimes this is given a spiritual aspect, like a female soul.

If he takes drugs to suppress testosterone and boost estrogen, he may start to believe that he is no longer of the male sex but is becoming female. Even more so if he elects to have surgery to remove his testicles and fashion his penis and scrotum into a non-functional cosmetic simulacrum of the female external sex organs. Some of these males even start to believe they're having a menstrual cycle, despite lacking any anatomy involved in this process.

However he reaches these conclusions about himself, every single one of these beliefs is false. These are delusions.