Have you considered that this is a thing that's probably true of half the audience of Doctor Who as it stands?
At any rate, livid may have been glib, but I stand firmly by irrational. You have reasons, but they're rooted in emotional reactions and not rational ones. One of you doesn't want the Doctor to be female because, in spite of the show saying clearly that Time Lords can change gender in regeneration and accepting that, you believe that The Doctor's gender is essential to his nature. The other doesn't want him to be female because you don't want to lose some kind of exclusive hold on relating to the Doctor you currently feel you have. Neither of those are rational reasons for wanting him to not change.
And male protagonists will never ever go away. They are not a disappearing species in need of protection.
Agreed. The Doctor's ingenuity and personality is what is integral to the character, not necessarily the gender. It would seem pretty obvious to me that, as fair as the series has generally been (compared to many, many others), it has still maintained a purely male lead for specific, gendered reasons.
At the same time, I don't want a female doctor just because it's an antithesis to the mold, and I feel like it would be interpreted that way due to the subtle (and not so subtle) ways in which Doctor Who/Torchwood has pushed a variety of gender/sexual relationships to the forefront in recent years.
I want to see it happen because I honestly think it would be an interesting twist on the story of the Doctor that hasn't really been tackled yet. But once again, it is the Doctor's "nature" that makes the character so easy to idolize. I hate this argument because I feel that it, oddly enough, only really matters to the adult male fans of the show. Kids who love Doctor Who, and (I realize I'm making a bit of an unfounded leap here) a large portion of the female audience would undoubtedly still watch and enjoy it if the Doctor was a she.