As long as we have religions that advocate mindless reproduction just to keep their dominance, you will never end the acceleration of human reproduction.
Most humans want kids, its in our nature, but if all humans have 10 kids each, and they get 10 each... etc etc. you will come to the realization that growth in human population is unstoppable without some cataclysmic event or totalitarian master/slave society where only the top gets to reproduce.
I pick the indiscriminatory cataclysmic event any day over elitist governance over the right for reproduction.