That's clearly untrue. Most of the world's democratic countries no longer have growing populations by birth rate. All the growth comes from immigration. In some countries this is already causing issues as the working aged struggle to support the welfare requirements of the ageing population. In some of the high population countries there is a clear shift of the younger more affluent generation from country to city where larger families are a hindrance (cost) rather than a benefit (extra hand on the farm).
It won't happen overnight but based on current trends population will peak in the next 30 years and then start falling. Population growth, from this point forward, isn't the primary issue.
