"Problems with the new doctor"
Alright, here we go:
-Time Lords changing genders is something introduced in NuWho, and introduced quite clumsily at that. More on that later. By the time the concept was introduced, we'd had 13 male Doctors. It's a bit late to assume that this is anything but the norm, that the Doctor is male. The show also seems to want to have its cake and eat it by stating that Time Lords don't care about gender like humans do (which is a a false equivalency, as humans can't change gender bar artificial means), but we've seen cases where the Time Lords do get caught up on it, such as the General (after going from male to female, utters "back to normal. Seriously, how do you [male Time Lords] stand the ego?"), or The Master ("is the future going to be all girl?"). There's also examples of familial terms being based on gender - Susan is unambiguously the Doctor's granddaughter (and her her grandfather), Jenny outright calls the Doctor "dad," the Doctor is River Song's "husband," etc. How do those familial terms remain relevant
-Every gender flip we've seen so far is from male to female. Thing is, I know we've had people asking for a female Doctor since at least Eleven (no idea why, struck me as asking for a female James Bond or a male Wonder Woman), but if the show really wants to go down the route of Time Lords being gender fluid in regenerations, not only is the revelation coming a bit late, but it's a revelation that has shown gender flips go in only one way. I for one was never asking for a male River Song/Rani/Jenny/Romana, and I'm not even asking for them now.
-There is, to me, a sense of agenda behind it. I really don't want to dwell on that, but let's look at this from the opposite end of the spectrum - if you want more women in TV/film/whatever, is appropriating a previous character/franchise really the way to go about it? I'll be frank, if they outright killed the Doctor off or retired him, I'd be more reciprocal to a show with a new Time Lord, because at least said female Time Lord could stand or fall on her own merits. If you want more women in media, fine, but at least put in the legwork for it. Off the top of my head, Star Wars. Like her or loathe her, Rey, while having a lot of similarities with Luke, at least had the legwork put in for her, building a character from the ground up.
Thing is, outside Doctor Who, I'm iffy of the precedent this sets. Doctor Who at least has some wriggle room for a gender flip, but when you start getting into characters that are definitively male (James Bond, Indiana Jones, etc.), what happens when the "SJWs" go for them and start demanding female takes? Thing is, I'd argue that James Bond and Indie have already had gender flips done right in the form of characters like Lara Croft and (to a lesser extent) Kate Archer. Female characters that take inspiration from male predecessors, but are still able to stand on their own legs. Or, in other words, the introduction of Lara Croft to the world didn't mean that the world stopped being able to enjoy Indiana Jones, whereas a 13th Doctor is mutually exclusive with a male one. So in the realm of agendas, no-one's served. Not the people who see the Doctor as male, nor the people who want a female Time Lord have her own show.
-There's the question of Missy, which encapsulates this point for me perfectly. Thing is, as a character, I liked Missy. As an incarnation of the Master? Eh...not so much. If anything, I feel that idea undermines the Master because not only does his redemption of sorts with Ten fall hollow now (yep, back to evil), but is it out of the question that the Doctor had other childhood friends that went bad, who'd he want to turn good? Missy being the Master is at its most poignent in the "we stab each other in the back" moment, but even then, you could have still gone with an earlier version of Missy that was already bad and get the same result. So while I'm sure I could enjoy the 13th Doctor as a character in of herself, as THE Doctor, the definitive article as it were? Not so much. Basically the problem of engagement I had with Missy, now transferred to the main character.