Your spiel runs into a brick wall when you discover what the Supreme Court (
Casey decision), and practically everyone else, has already said: women don't have abortions because they can't get contraceptives;
they have abortions when their contraceptives fail.
Statistically, if a girl goes on the pill when she's 15 and has sex regularly, according to the real-world effectiveness stats, her chances of getting pregnant at least once before she's 25 are 100%.