At this point, there is no definitive answer as to the cause of the congenital disorder called transsexualism. Even though there are only tiny differences between the brains of males and females, those differences are important, especially the one that tells us whether we are female or male. There is evidence that the brains of those born transsexual are more like those of the sex they say they are than those of the sex their anatomy dictates. And it's reasonable to assume that the brain and body in these cases were virilized (or not) differently, since hormone-induced changes to the brain happen at a different point in gestation than hormone-induced changes to the rest of the body.
Still, no one knows why this happens. And some are determined to find some kind of reason—or perhaps justification would be a better word.
So some look at chromosomes. Somewhere between one in 500 and one in a thousand boys is born with the karyotype 47,XXY or its variant 47,XXY/46,XY Mosaic (meaning some cells have 47 chromosomes while others have 46). Those with 47,XXY are anatomically male, except in extremely rare cases (which happen with 46,XY as well) in which the SRY gene is not expressed on the Y chromosome. It's the presence and activation of SRY that determines maleness. The extra X chromosome does not change this.
All boys born with a 47,XXY karyotype have certain characteristics that are not overt, such as lower fertility. Some also exhibit certain physical characteristics, which are called Kleinfelter Syndrome (Kleinfelter Syndrome is not a synonym for 47,XXY). Regardless of symptoms, which can include gynecomastia, those with 47,XXY (minus the rare exceptions) are all male. Even though it is usually classified as an intersex condition, it is not so in the same sense as something like true hermaphrodism is. There are no female reproductive organs present as a result of 47,XXY (although 47,XXY can be co-morbid with other intersex conditions).
Nonetheless, 47,XXY and 47,XXY/46,XY Mosaic are sometimes trotted out to explain transsexualism. The lack of correlation does not stop people who feel a need to justify their condition, nor does it stop certain media from taking such justifications at face value.
Some with 47,XXY are also transsexual and change anatomical sex from male to female. But most who change anatomical sex from male to female are 46,XY, and most who are 47,XXY are not transsexual and do not change sex. Whatever causes transsexualism, it is independent of the number of chromosomes or the presence of an extra X.
It is unfortunate that misinformation abounds—that 47,XXY males are "partly female," that 47,XXY males are more likely to change sex, that 47,XXY explains sex change. A woman born transsexual (male-bodied) whose karyotype is 47,XXY and who exhibits typical Kleinfelter symptoms such as broader hips, less bodily hair, and gynecomastia might well end up being pleased with those symptoms, but the characteristics are only coincidentally feminine. They neither cause nor compel a sex change. There are also 46,XY nontranssexual males who have gynecomastia, whose hips are broader than normal, who have less bodily hair, whose testosterone levels are lower than normal, and whose fertility is reduced.
Transsexualism, as rare as it is, exists in people with 46,XY, 46,XX, 47,XXY, various Mosaic patterns, and pretty much any other viable karyotype that exists. Just as most people with 46 chromosomes are not born with transsexualism, most people with other chromosomal arrangements are also not born with transsexualism. If someone born transsexual feels a need to justify changing sex, they should seek the justification elsewhere rather than promulgate harmful misinformation.