Well, in all fairness to the WH, they did say they were looking for a woman. Which is still strange, because Alito and Luttig were just academic choices, then.
I think there are very few in the Republican base who care whether the nominee is a woman. Obviously Laura Bush does.
I assume there is some technicality in the law that allowed the WH to consider women only? After all, if I advertised a job opening as "Women Only" or "Men Only" I'd be sued.