I really don't see why it's a very bad answer, though I understand the attraction of "simply yes." I'm drawn to "simply yes" when I focus on transgender memoirs like She's Not There, by Jennifer Finney Boylan (she's delightful on "I am Cait" in episodes 2 and 3!) and these compelling videos by Standford psychologist Ben Barres.
The other answer gets you to the same place, practically speaking. "Politically yes" means something like: people are entitled to their own gender-spectrum decisions. It's up to me whether I'm girly or not girly, not girly or androgynous, androgynous or downright butch. I get to cross over from one spot on the spectrum to another, if I like--even going all the way from female to male--and have my decision socially respected. When it comes to our gender identity, we have "first person authority," as Talia Mae Bettcher puts it in "Trans Identities and First Person Authority." By this, she doesn't mean we know a fact about ourselves, introspectively, but that it's up to each person to choose a gender presentation and everyone else's duty to respect that choice.
I would add "ontologically I'm not sure" to "politically yes" because I'm not clear that a person's choices, gender-wise, create the sort of robust facts that could make it simply true that Boylan is a woman and Barres is a man. If it were simply true, what would the truth of the matter hang on? One option is to say Boylan has a female brain and Barres a male brain, but to the very limited extent that brains are dimorphic, they're dimorphic with respect to a little bit of reproductive machinery (see this, by Donald Pfaff), and Boylan is presumably the one with the male brain, Barres is presumably the one with the female brain.
Apart from a little bit of reproductive machinery, brains are a mixture, with males only statistically leaning toward certain traits and females to other traits (see this, by Daphna Joel). Even if Boylan's brain leans female (does it?) I don't believe it really makes sense to say that a brain with lots of traits that are a little more common in females is a female brain; or a brain with lots of traits that are a little more common in males is a male brain.
Another option is to say that the truth of the matter hangs on gender identity feelings. So a male is someone with a sense of being a male; a female is someone with a sense of being a female. This seems like at least a possibility, but there are legitimate worries. A lot of people don't spend a whole lot of time feeling like members of their gender. We're encouraged to do so, but some resist, and some just don't. Or maybe we do, but gender identity recedes very far into the background? It's quite possible that there are more vivid gender identity feelings in people who find their gender complicated and difficult.
Loose analogy. I once sat at a table of 12 Jewish women discussing whether we believed in God. We all went around expressing one degree of skepticism or another, and then came to the last person, who had converted to Judaism. She believed! Her transition to Judaism had given her a rather different experience of being Jewish than the others had. In order to ensure her inclusion in the class of Jewish people, you could say having Jewish beliefs is definitive of being Jewish, but then the other 11 of us would be excluded! I worry that defining gender membership in terms of gender identity feelings could possibly have the same effect.
Perhaps being Jewish is actually a disjunctive property--you have it based on parentage OR based on beliefs. Could gender be similarly disjunctive--you're female based on gender identity feelings OR simple biology? That sounds attractive, but what's going here if we take the disjunctive route? Are we really getting at realities as to who belongs to which gender category (or religious category) or have we entered the realm of ethics and politics? Is there really a class of entities that share one property-- female--based either on having a sense of being female or female biology? Could the femaleness instantiated in these two ways be the very same property?
Certainly the ethics and politics here is far simpler than the ontology or metaphysics. Yes, as far as social practices go, trans women are women (and trans men are men). We're entitled to be self-determining gender-wise, and to have our self-determinations socially respected. As to the underlying ontology or metaphysics, that's more puzzling, and sure it isn't a bad thing to be puzzled about what's truly puzzling, instead of having a settled view.
More links: on the metaphysics of gender, I've found this anthology useful. There's some interesting stuff about trans identities, including the Bettcher article, in "You've Changed," edited by Laurie Shrage. Especially interesting is the article by Christine Overall, "Sex/Gender Transitions and Life-Changing Aspirations."