You say privacy has nothing to do with abortion. I would say your argument is not with me put with the Supreme Court ruling in Roe vs. Wade which drew its conclusions very much from the previous ruling of Connecticut vs. Griswold.
The SCOTUS ruling used privacy as the reasoning for striking down all state abortion laws. Abortion laws which were arrived at by proper legislative action and not by court fiat.
I am pro life and would rejoice to see Roe vs. Wade overturned. At that point the question should return to the States. I don't doubt to my sorrow that some State's would have liberal abortion laws. As they did before Roe vs. Wade. But at least then the pro life movement would have a real chance to see progress in fighting against carte blanche abortion.
I'm afraid we've never going to get the abortion genie back into the bottle. There will always be states that will allow it, if their citizens vote to do so.
The biggest difference today is that with the issue so much in the news for the last 30 years, that opinions were formed early on, then changed, as information trickled in. At first, the abortion thing was argued as a 'woman's right to choose' and was all bound up in the zeitgeist of equal rights for women, and new choices for women. At the time, all the media outlets were behind the 'right to choose' and filled the airwaves with the idea, all the time portraying anyone who was pro-life as a religious zealot, or a man who was trying to keep women from 'fulfilling' themselves in their careers, etc.
I think the tipping point came with actions of Operation Rescue. The Rescues made the national news, and suddenly people in this country began to see the face of the pro-life movement, and realized that they had been lied to by the media. The people being hauled into paddy wagons didn't have horns, and most were NOT men! There were young people and old people, male and female. When folks saw someone who looked like their Granny being carried by her feet and legs by police to remove her from a protest, it got them to pay attention to what Granny was saying. The polls began to move more to the pro-life side, and have continued to do so.
Most folks nowadays seem to be of the opinion that abortion should only be done early in the first trimester, and should only be used in severe cases, like rape, incest, and in the event the LIFE of the mother is threatened. They are heavily AGAINST abortion for birth-control purposes, and abortions of babies after 20 weeks or so. They've seen too many 24 week preemies, not only surviving, but thriving, with the help of modern medicine.
What people have to be made to understand is that when Roe-v-Wade is overturned, it will not automatically make abortion illegal all through the country. It will simply return to the status quo ante 1973, and the states that allowed abortion will continue to do so, and the citizens of the other states will have the right to determine for their own populace, the status of abortion in their states.