There are many reasons, not having access to family planning, sex/reproduction education, contraceptives and abortion services does increase the birth rate.

Culture still plays a major role in these dynamics though. Educating women and empowering them to have more choice in their own reproductive choices has decreased the birth rate in some areas. The problem with that though is that you do have to educate men as well, as culturally, they make the major decisions in regards to reproduction. The issue is about empowering women culturally via education and economic opportunity.