The search continues. Ross Douthat hasn't completely outed himself as another anti-contraception nut, but he's getting closer by denying that contraception reduces the abortion rate by attacking the cause of the vast majority of abortions, which is unplanned pregnancy. He's smart enough to realize that openly peddling anti-sex ideas like depriving women of contraception discredits him, but this silly idea that contraception doesn't affect the abortion rate is straight out of the mouth-breathing anti-sex hysteria pushed on more openly crazy Fetus People blogs and in Catholic marriage classes.
What's actually controversial is not that using contraception will mean you get less abortions, at least amongst intellectually honest people. (It's worked for me!) What's controversial is whether or not banning abortion will really do much to reduce the rate. I suspect at first it would, but as women taught each other ways to obtain illegal abortion, that wouldn't be true. Actual historical research such as the kind you find in Leslie Reagan's When Abortion Was a Crime shows that the only reason anti-choicers can pretend that the abortion rate was low in the days before reliable contraception is that abortion was illegal and untracked. But just because they weren't tracking it doesn't mean it wasn't common. In fact, it was the only form of birth control for many, perhaps most women. Reagan reports a world where women would slip off to the abortionist on a routine basis. It wasn't talked about much, but I suspect for a lot of women, having 5, 6, or a dozen abortions over the span of their lifetimes wasn't unusual in the slightest.
Nor, unfortunately, was death from botched abortions, particularly those caused by young women with few connections or resources trying to self-abort. The notion that illegal abortion wouldn't cause massive safety issues is one that the right has started to peddle, but that comes from a misunderstanding of how women botch it in the first place, which is usually by trying to do it alone and by themselves, because they have no access to an abortionist. Dying from a botched abortion is a particularly gruesome sort of death, usually visited on very young women, and it's slow, painful and the victims often suffer and even die alone, too terrified to summon for help. In her book This Common Secret, Susan Wicklund describes such a death that happened to her grandmother's friend when her grandmother was a teenager and tried to help her friend abort. I defy anyone to read about such deaths and deny that it's a deep, sick misogyny that would arrange policy to make sure that such deaths become frequent again.