(revisiting this topic) Great question, Stephanie! And the fact there's as yet no definitive answer is VERY interesting.
This morning I started reading Kate Borenstein's Gender Outlaw (one of the books I bought as study material for transition.) I'm a little over halfway through, and I haven't found an answer to your question there, but the questions Kate asks and the viewpoints she puts herself and the reader in are good for framing the question you asked.
Society defines gender as either/or. Kate makes the case that it's a multi-dimensioned continuum with two nodes around which most people cluster, or are forced to cluster.
Further, she presents society's gender rules, as stated in Harold Garfinkle's book, Studies in Ethnomethodology--
1. There are two, and only two, genders.
2. One's gender is invariant.
3. Genitals are the essential sign of gender.
4. Any exception to two genders are not to be taken seriously.
5. There are no transfers from one gender to another except ceremonial ones.
6. Everyone must be classified as one gender or another.
7. The male/female dichotomy is a 'natural' one.
8. Membership in one gender or another is 'natural'.
And I personally think the above rules are so much organic fertilizer. But in general, society has internalized these rules and will agressively defend them. Which is why so many T-women are virtually obsessed with passing (myself included.) If you're caught violating the rules, you're punished.
But this still doesn't answer the question what 'makes' one Female.
Maybe we can get to the answer by asking what ISN'T Female.
Generally, it seems;
Males TAKE. Females SHARE.
Males are territorial. (HELP! Is there a Female trait that's the converse for territorial?)
Males see others more as objects to be used, Females see others more as people to be related to/with.
Males organize by determining who leads and who is led, and then performing in those roles (a weak male will enhance his power by choosing a powerful leader to be led by -- one of the reasons males intensely identify with powerful sports teams, I suspect.) Females organize by conspiring and co-operating.
Feel free to add to this list -- it's only a start.
Is being Female a willingness to be vulnerable? One of the cliche bits of feminie body language is holding the hand back in such a way the wrists are bared (and it's interesting that this is seen as displaying vulnerability.) In fact, much 'feminine' body language and body positions can be seen as showing vulnerability. And why vulnerability? Is it because it triggers a protective instinct? (JOKE: Why are babies so cute? To keep ya' from killin' 'em.) I don't know the answer, I just ask the question.
Is it a desire to be nurturing towards others?
Is it being more open to touching/being touched, hugging/being hugged by those who we allow to be close to us? Is it being more open to (non sexual) intimacy with those we are close to?
I know I have more questions, but I can't articulate them just yet.
Dammit, Stephanie, you asked a really good question!
Haz