There's no such thing as a transgender person because gender doesn't apply to people, it applies to language. Words have gender -- masculine, feminine, or neutral -- humans have sex -- male or female. It's a very simple issue, either you have a Y chromosome or you don't. Science has settled the matter.
OK. It's not quite that simple, sex is determined by the gene, SRY, which is a testis-determining factor. This gene is almost always carried by the Y chromosome (more on that below).
The promoters of the "transgender" agenda will sometimes refer to exceedingly rare birth defects like Klinefelter or XX male syndrome to buttress their case. But this argument is based on the wrong assumption that sex is determined by genitalia. As noted above, it is not, it's determined by genes.
Those who suffer from Klinefelter syndrome are born with two X chromosomes and one Y (XXY). This makes them technically male (sterile) but with some feminine manifestations.
XX male syndrome is a little different. Because of unequal crossing over between X and Y chromosomes during meiosis in the father, the X chromosome, passed on by the father, contains the SRY gene. As with Klinefelter sufferers they are technically male (and sterile), with feminine manifestations.
Both of the cases above represent exceedingly rare birth defects. In the case of Klinefelter syndrome about 0.03 percent of people will have the condition. XX male syndrome is even rarer -- less than 0.005 percent of population are afflicted.
As you can see, being male or female isn't about how you "feel", it's determined by genetic reality. If you "feel" like you're a woman inside a man's body (or the reverse) that doesn't mean that you are some heretofore undiscovered "gender", it means you suffer from a mental disorder.