Damon (Linker), and many others who participated in that Facebook thread (about abortion), voiced the belief that America has far more abortions than it otherwise would because conservatives are not doing enough to give women better access to contraception. This belief seems intuitive -- after all, birth control keeps you from getting pregnant, and it's hard to get an abortion if you're not pregnant. But when I look at the data, I am reminded of Ambrose Bierce's definition of prejudice: a vagrant opinion without visible means of support.
Consider abortion rates in various developed nations:
The U.S. rate is certainly high compared with, say Germany or the Netherlands. On the other hand, it's lower than Sweden, and right around that of New Zealand and the UK -- countries with comprehensive national health-care services that provide birth control. And who had one of the lowest abortion rates? Ireland, where it was illegal. (Irish women travel abroad to get abortions, but the rate still seems to be quite low by international standards.)
Now, obviously, we could theoretically do something to reduce our abortion rates to more German levels without going so far as to ban it. But this data doesn't really suggest that "something" is necessarily "provide more affordable reproductive health care services to women," or indeed, anything else that lends itself to government intervention, such as "better sex ed." Extremely high abortion rates can coexist with extremely comprehensive health-care systems and liberal social norms.
You see a similar pattern in the U.S. when you look at the variation in abortion rates between states: Liberal blue states with liberal abortion laws and liberal attitudes about birth control
seem to have the highest, not the lowest, rates of abortion. What drives this? I can come up with a number of plausible theories, but I couldn't tell you which one is right. On the other hand, I think we can reject the hypothesis that liberal attitudes toward sex and birth control are a surefire way to get the abortion rate down.
In fact, the evidence for this thesis was never very good. Even William Saletan, who used to be a leading advocate of the squishy pro-choicer thesis that abortion is terrible so we need to give people lots of free birth control, ended up abandoning this thesis when he concluded that there's just not good data showing that the high price of birth control, or the inability to get your hands on the stuff, is the major reason people end up having abortions.