He justifies the 1960s era fear of the population bomb and his explanation is more robust than cultural exposure such as television. Namely 1) economic factors: Market responses, innovation (especially the green revolution), globalization and 2) demographic factors: urbanization, fertility decline and investment in children.
When we see growth rates of food output or GDP of 7% and 10% per year we can see how countries like Vietnam, China, and India outraced the Malthusian devil in recent decades. The point is not that population growth does not create challenges for economic development, but that these challenges can be overcome when forces like market liberalization lead to this kind of rapid economic growth.
It may seem that fertility decline alone is a simple explanation for surviving the population bomb, but this would undermine the effect of economic factors and incentives on fertility. Even as someone who studies the effect of simple access to family planning on fertility, I know they're all related.
Hat tip: NAJ, DL