Access to birth control prevents unwanted pregnancy. Fewer unwanted pregnancies likely means fewer abortions. A study from the Washington University School of Medicine revealed that women who had free access to birth control methods "were significantly less likely to have an unwanted pregnancy or induce an abortion and were more likely to be adherent to treatment". Fewer abortions is beneficial to the overall mental and physical health of women. Choosing abortion takes a terrible toll. Removing barriers between women and birth control instills habits that will last until far into adulthood, allowing women to choose if they have children, and if so, when.
Access to free birth control doesn't mean that people will use it. We cannot guarantee that the responsibility of users will increase with the removal of barriers between them and birth control.
[P1] Access to birth control creates fewer unwanted pregnancies. [P2] Fewer unwanted pregnancies means fewer abortions and healthier women.
Rejecting the premises
[Rejecting P2] We cannot know that this is the case.