Many transgender people have to deal with a dual identity, having the body of one gender and an internal gender identity of another. Traditionally, in Western cultures, we only allow for either "male" or "female". However, gender identity is a fluid construct - things that at one time where considered masculine are no longer thought to be masculine (i.e., wearing frilly shirts and powdered wigs in the 18th century). Some transgender people manage to keep both identities pretty much separate, others become extremely stressed and make changes to their apparent gender identity, and still others, unfortunately, cannot deal with the stress and commit suicide.
I feel that each person has some degree of masculinity and femininity. Internal forces (i.e., chromosomes) and external forces (i.e., societal norms) influence how individuals express their gender identity.
I realize that this is different than someone being an American from Texas and being a Texan first (or second), but this is more of a complex issue than what many people realize.