The transgender argument

Often while I'm driving I come up with a lot of thoughts. I've been thinking a lot about explaining transgender to people and this is what I came up.

The argument for those who don’t understand how a person can be transgender:

If I stripped you of your anatomy, would you still identify as a male/female?

(I assume the answer is yes)

A Transgender person is a person who when stripped of their anatomy they identify differently than the anatomy in which they were born. Just like your identity is independent of your genitals, so to the transgender person.

That is what I came up with. Any thoughts? Improvements? Am I completely off? I have another way of explaining it that is longer and more involved, but I thought this was a nice definition.