Even the kind of fictional character the Doctor is, is prototypically male: the eccentric mad scientist. None of the Doctors was madder or more eccentric than Tom Baker’s Fourth, with his teeth and curls, impossibly long scarf, and penchant to offer jelly babies to everyone he encountered. The Eleventh, as eccentric as ever, described himself as a “mad man with a box,” a box that travels anywhere in time and space. An eccentric woman is Eleanor Abernathy.
Each Doctor has a different personality and temperament. So too will the 13th. Yet by making the Doctor a woman, new showrunner Chris Chibnall and company have placed themselves on the horns of a dilemma. The 13th Doctor must be different, but in ways that cannot be immediately attributed to her biology. For if she is different in ways that can be chalked up to her being female, then it does make a difference that she’s a woman. Whereas the whole point of casting a woman in the role is to prove that it doesn’t matter. (Though I suspect those who spent the past decade advocating the change rather think it does.)
The Doctor can be a woman because there’s nothing special about being one. There’s nothing unique or significant about womanhood. It’s not an essential trait or characteristic — and that is the only way the Doctor can still be the Doctor while being a woman, that it is something indifferent. For if the Doctor changes in some fundamental way because he is now a woman, then he won’t be the Doctor any more. Which would mean, therefore, that in fact the Doctor can’t be a woman. Hence the dilemma.