One of the arguments contraception opponents commonly make is that the acceptance of contraception leads to abortion. For a good debunking of that argument, read "Examining the argument that provision of contraception leads to increased abortion rates".
What leads to increased use of both contraception and — especially when contraception is unavailable or inadequate — abortion is the desire for relatively low fertility. Contraception and abortion are going to be much less of an issue when people fully expect to have six or eight or ten kids. Those days are over for most people in the developed world, for complex social and economic reasons. What we have to decide now is whether we're going to deal with that reality in an evidence-based manner, or pretend it's not happening (or that it shouldn't be happening, and therefore people who want to have sex but not have a lot of babies are just immoral).