She is just following orders to stay out of the fight. And since she's a far better medic ninja, her duty is to save as many as she can by tending to all those hurt in the blast. Not to mention the fact the Hokage needs healing since she can't heal herself after she used her stored chakra to help everyone hurt already.
As for Kishi hating women...he did make a woman Hokage. And made Jirayah a total pervert and it's for that reason Tsunade knew he's not a one woman kind of man.
And Sakura's character did amazing that while she was strong for being 16 and the old lady Chiyo being well...too old. They each alone could not face Sasori but combined they could. That wholly revolves around with the team effort that Naruto is about. It was harmonious in that Kishi wrote what can become when a hand of old and young come together to fight. Knowledge and youthful stamina.
The way I see it, Kishi is not only a story teller but in that as a writer he can explore the depths of human nature in friendships, hardship, and love lost and love won.
And since there is so many characters he can only use so many at a time for a sequence. And along the way as he writes, he gives us glimpses of something that just might or might not be there.
In order to bring all of them to life (and this is why we love the Manga to begin with) he is merely showing the fact that sometimes life isn't fair no matter how much we want it to be.