Guardian op-ed writer and feminist Claire Budd makes the argument:
I’ve heard some funny comments this week, Dr Who being racist, sexist and not dealing with real issues being three of them. Having watched hours of the programme and its spin off series The Sarah Jane Adventures, I’ve heard all of those issues being dealt with beautifully. And episodes like Richard Curtis’ 'Vincent and the Doctor', which tackled the taboo of mental illness, have given me some great material to work with as a mother. Not to mention the introduction of many other historical figures – bringing them to life and making them interesting – as well as the parts of our story written into the Doctor’s adventures, including slavery and the stealing of natural resources.
But by far the most valuable contribution to the younger generation has to be the fact that the Doctor is the only non-violent “superhero” male role model. He solves problems through talking and he’s proud to be a science-loving, socially awkward geek. He’s the hero of boys and girls. But most of all he shows boys that violence and aggression won’t get them what they want. Being clever, not conforming, being kind, talking – these are the ways to be a hero.
This comes directly from speculation about Matt Smith's departure. I've heard arguments on both sides now, and I have come to the conclusion that as long as the actor playing the Doctor remains true to the role, it doesn't matter whether the Doctor is male or female.