...However, this isn't what people are talking about when they compare transgenderism to the imaginary phenomenon of humans deciding to call themselves dolphins, or of Anglo people suddenly deciding that they're Asian "on the inside." When people draw this comparison, they're pointing out that they simply don't understand what gender is, and that they have confused sex (physical traits) with gender (behavioral traits). They've also confused the desire to transition-- something that trans people do so that they can function without ridicule and "pass" for their own gender-- with a cosmetic, delusional, or curious urge to have a different kind of body.
My four-year-old daughter occasionally tells me that she is a dog, a train, a dinosaur, or an elf. These are not real identities, because these make-believe personas are based entirely in a set of traits that my daughter simply doesn't have. My kid is not, and will never be, a transspecies tiger. My partner, on the other hand, has all the traits associated with the female gender, even though she lacks the traits associated with the female sex. I'm confident that I can take my partner's identity as a woman seriously, while interpreting my daughter's idea that she's a pony as exactly what it is: a fun fantasy.
(Disclaimer: I work for Yahoo!. My job doesn't include posting this here. I found it very moving and have cited it frequently in conversations since it was published, so I thought I'd share.)