There's some truth to it. Surely there would be more abortions if all birth control suddenly disappeared tomorrow (see communist Romania, for example). The issue is that it comes down to marginal returns. As it is now, birth control is already very easy to get across America. Very few women have abortions because they couldn't get birth control - either they chose not to use it, or they tried it and it didn't work (all methods have a failure rate). So making birth control even easier to get won't do much, if anything, to reduce the abortion rate. On the other hand, abortion laws throughout America are very permissive (save for Texas and Oklahoma). Making abortion illegal would do a lot to reduce the number of abortions, because it largely hasn't been done. As it turns out, one of the ways they work is by giving people an incentive to use the most effective forms of birth control.
Interesting that pro-choice people trumped up IUDs as the best thing in the world during the late Obama era, yet now they seem to be sad that more people are using them. Whatever happened?
https://www.washingtonpost.com/lifestyle/2022/05/10/iud-birth-control-supreme-court-draft-opinion-leak/
https://secularprolife.org/2015/07/women-in-pro-life-states-use-better/
Interesting that pro-choice people trumped up IUDs as the best thing in the world during the late Obama era, yet now they seem to be sad that more people are using them. Whatever happened?