I think that the 12th Doctor should be a woman.
I would love to see the 11th Doctor change genders in the regeneration process and then be played by a female actress. Here's why.
First reason, yes, it can happen. There are absolutely stories of time lords switching gender back and forth from regeneration to regeneration. Case in point, The Corsair, a time lord whom The Doctor had known as both sexes. The 4th Doctor mentions The Corsair as being both male and female, as does The 11th Doctor.
Second of all, think of the way The Doctor is cast. The role is so incredibly unique and wonderful that incredible actors become The Doctor. Actors that haven't broken through yet, but they're amazing. Actors who have had some moderate success, but they're better than that. They SHOULD be mainstream hits. Imagine the impact that playing the 10th Doctor had on David Tennant's career.
He was waiting, on the cusp, such a dedicated actor that conveyed such striking conviction in his roles. The world now knows him, because of Doctor Who.
That being said, they would find an incredible actress to play The Doctor. We, as Whovians, would get to watch another incredible career unfold.
Third, the show needs more male companions. Captain Jack, Rory, Craig, where's the next one? Where's the next person I can't wait to root for? Who's going to save their child next while being imprisoned in an iron suit? Who's going to become the friend that The Doctor finds randomly throughout his travels, for thousands of years? Who will be the next one to tell him something like YANA? And then. Who is going to be the next companion to jump off a roof with his wife to save both their lives? I want to see, I want to know. A female Doctor lines everything up for a great new male companion.
Fourth, a simple wonderful example of the number one reason we are ALL curious as to what a female Doctor would be like, River Song.
You cannot be more badass than River Song. Her story arc was so incredible that someone made an infographic about it just to try and put it in a way everyone could follow. Everything from "Let's Kill Hitler" to The Library. I want to see more strong female time lords.
Yes, I'm aware that this probably won't happen for the 12th Doctor. That being said, it absolutely should happen in the coming years. Everything is changing in this world. If Doctor Who stayed the same, it would not be as appealing as it is today. The show has evolved over the last 50 years and shows all of us just how far the human mind can go. The writing, the acting, the sets, the effects, it's all evolved into what we have now. The time to strike has come. It's time for The Doctor to regenerate into a woman.