There’s only really one argument that is, if not convincing, worthy of some genuine contemplation: that the Doctor should be preserved as a male role model, being one of the most prominent fictional heroes who isn’t reliant on violence and aggression, but instead is a template for teaching curiosity and compassion to children.
It’s an understandable stance to take; obviously, children’s media is important, and it’s important to have role models in that media. There is something important in having a character who subverts more traditional norms of masculinity – a character who uses his brain rather than his fists. The argument goes that the Doctor is largely unique in this regard, and in turn that’s why the character should continue to be depicted as a man – because he’s the only man in fiction who is like that.
I am, of course, still going on about the possibility of a female Doctor. I fear I’m really setting myself up for disappointment when it ends up being… well, Kris Marshall! (I hope not.)
However, this idea of the Doctor as a male role model is the only argument that’s ever given me pause in my otherwise unrelenting viewpoint. So, I wrote an article about it!
(A year-ish later, and I have genuinely no idea what I concluded about. Well, I know what I concluded, just not how or why. Don’t suppose it matters much now exactly, though it might be interesting to see what anecdotal accounts spring up during the actual series itself.)
Oh, and the cosplayer above is Jacklyn Black, who is seemingly never credited whenever this very cool picture is used, so I figure I should make the effort to acknowledge her.