Sanger claimed that the availability of birth control would make abortion rare. That has to do, I think, with the reverse side of eugenics, which was that the “”upper classes,”ought to have children.” The Nazis taught the same thing. The superior breeds should not kill their young.
Abortion was relatively rare in her time.
However in her writings she claims that infanticide was being practiced in urban poor immigrant families (she was a nurse and social worker among these populations).
She did think that contraception would cure a whole host of social ills ... poverty, vagrancy, illiteracy, etc. Turns out she was wrong from what we know today, but in her day it seemed a reasonable assumption.