The shift to 'caring about women' is a public relations shift away from caring solely about the fetus. The idea can probably be credited to David Reardon of the Elliot "Institute" which has come out with many unscientific studies on how women are harmed by having an abortion.  

It is a strategy for both anti-abortion fever and evangelism.

This is from in interview with Father Pavone of Priests for Life in the 1990s.  The whole thing is:
here.

P: ...Can you talk a little bit more about how your work has led you to develop a strategy for the pro-life movement which in many ways is new.

R: On the political side we have kind of fallen in to the trap set up by the other side: a choice between helping the baby or helping the woman. Whose rights are more important, the baby or the woman? That's a false dichotomy. God joined woman and child together in such a way that to help one you have to help the other, if you hurt one you are going to hurt the other. It's unavoidable.

So we have to be much more vocal in expressing that we care about women not only before they have an abortion when they are pregnant. We care about them after they have had an abortion. We care about women. We want to protect them. If they are going to have an abortion and nobody can stop them, we want to protect them from the abuses of the abortion industry. We've got to show the American people that we are more pro-woman than the pro-abortionists...that we care more about them and their babies. And so I use the analogy that a marathon runner couldn't win a race breathing only with one lung. And sometimes the pro-life movement breathes with one lung for the baby -- but we need to breath with both lungs. One lung for the baby, one for the woman. Together they are a package and we have to care about both.

Now we are kind of actually in a situation where we have to play catch-up. We have focused so much on the baby before -- and I am not saying that we shouldn't focus on the baby or that we shouldn't talk about it -- sometimes people misconstrue what I say and think I am saying we should only talk about the women. No that is not it at all. But actually as we help women find healing, they are going to be far more effective talking for their babies than I am. I can talk about the scientific facts that a heart beats at three weeks and certainly that's true, but what is more important, what converts hearts better, is when a woman or a man who lost a baby says "my baby died in that abortion."

....So as we educate them about how abortion hurts women, it changes the whole equation in their minds. Their heart can soften now. This is why even pictures of aborted babies -- people harden their hearts to it because "I have already made up my mind, I'm for the woman." And so we have got to talk on what they are concerned about, the woman ... and help them see, well, don't you at least agree we should protect women from being pressured in unwanted abortions? Well yeah. Well shouldn't we make sure that women are screened for risk factors so they don't end up being hurt afterwards? Well yeah. So we can move them along slowly. And in that process their heart will thaw and they become more concerned about the women.

And on evangelizing:

There is so much joy after mourning and through the healing and coming back into the Church, and receiving the Sacraments with joy, and being free of the secret.

And so there is a tremendous opportunity and I think it is a great evangelization opportunity for the Church.