"Feeling like a female" is just that a feeling. It cannot be reduced to a performance, as set of personality traits, stereotypic interests or whatever it is people use to define what it means to be a woman or a man. And for transgender (and some intersex) people it cannot be reduced to genitalia or chromosomes either.
Yet here we are, those of us who experience this intense sense of misalignment, dissonance, incongruence. The feeling is real and I have come to the point where I use this feeling as the startingpoint for trying to understand this kind of transgender, instead of trying to explain it away with those invalidating words: "it is only......" (fill in the blanks: fetish, atuogynephilia, performance, fantasy....)
All of those "explanations" fail to address the intensity of this feeling and the complexity of the way it is expressed. All those observations that people use to invalidate transgender identities are, as far as I am concerned, effects of such a fundamental indentity. The fact that transgender identities can be express by so many means (crossdressing, fiction, performance, body alterations etc.) tells me that the underlying phenomenon cannot be reduced to either of them.
We can use those pehnomena to triangulate what it is, though, even no researchers have come up with the final explanation so far. Even the trans-friendly researchers too often end up in understanding gender identity as the sum total of gender stereotypes.
I suspect this fundamental feeling of being gendered is based in some kind of inborn need to orient yourself in the world as a gendered being, as a man or a woman or neither. The main difference between us and many other mammals is that in our case the strict behavioral patterns have been decoupled from this drive towards taking your place in society as a man or a woman (or something else).