Why does he have to nominate a woman?
Because "there has to be" at least one woman on the SCOTUS, just like in the past there "had to be" at least one Jew (the 3rd seat occupied first by Cardozo, then by Frankfurter, Goldberg, Fortas, Blackmun, who was the only non-Jew in this seat, and now by Breyer is even sometimes called "the Jewish seat") and at least one Catholic. Now we have a "black" seat (do you really think GHWB would nominate Clarence Thomas if it wasn't Thurgood Marshall who retired?) and it's rather obvious that there is one place reserved for a woman. Affirmitive action has applied to the SCOTUS appointments for a very long time, I'm afraid.
He does not HAVE to, but it is time. There are many qualified women just as good as Roberts and Alito.
Why take the risk of tweaking HALF the population, and exposing oneself to false claims of insensitivity to women?
It would be foolish to do such a thing. It will be a woman.