The problem here is that it is not necessarilly the woman's body, as there is another human being inside of it, or at least after a certain point. And if the State sanctions the killing of human life, that can lead to a dangerous slippery-slope. They allow what is essentially infanticide in the Netherlands, albeit under the guise of killing babies deemed to have health issues, and there was recently a journal article talking about how "abortions" of new-born babies should be permitted for any reason (
LINK). A baby can be born as early as 24 weeks, although that is asking for trouble. Over 90% of babies born prematurely in the third trimester and up (starting at 28 weeks) survive. Which means that it clearly is a baby a good deal before being born. There are varying views on this issue: some say it's a baby at the moment of conception, but are okay with birth control, some are completely against birth control as well, others are okay with abortions during the first trimester and part of the second trimester, but want them banned during the third trimester except if the woman's life is in danger or the baby has a condition where it won't live more than a few days after being born, and some want no limits whatsoever on abortions during any trimester.
We can see the slippery-slope to eugenics among the far-left mindset. If you can argue for third-trimester abortions with no limits, then you can stretch it to allowing the killing of new-born babies as well for reasons of a health defect (as is permitted in countries like the Netherlands). If you can justify the killing of new-born babies for health defects, then you can stretch it to justify the killin of new-born babies for any reason (as the article claims). If you can justify infanticide, then you can stretch it to justify forced sterilization of people deemed "unfit" to reproduce (this happened during the 20th century in the U.S.). Taken to its extreme, you get what the Nazis did (round people up deemed "unfit" and systematically exterminate them).
How the State views human life is akin to how it views freedom of speech. Is free speech something cherished as sacred to a free society, something that the government can only infringe upon in very limited circumstances? Or is it just a priviledge that can be infringed upon anytime the government wants if you start saying things they don't like (as it is in certain other so-called free countries). In America, it is considered sacred. So how is human life viewed? Is human life viewed as something sacred and cherished, that the State can only end in limited circumstances, or is it something that the State can decide as it pleases?