Population growth in almost all countries in the world, including the United States, is not a myth. Dinesh D'Souza (of the infamous American Enterprise Institute) and his friends may have chosen to have only one child, but nevertheless the population of the U.S. is growing by about 2.5 million per year. Of that, immigration contributes about 1 million. Even disregarding immigration, the natural growth rate of the U.S. population is about 0.7% per year, which is higher than in any other developed country (the rate in the U.K. is 0.2%). Using the U.S. Census Bureau's "medium" projections, the U.S. population will increase to 394 million by the year 2050. Even the "low" projections show some increase, and the "high" projections show an increase to 519 million.
Another dangerous myth is that one may predict the population in any country in the next hundred years strictly on the basis of the average fertility rate. Many other factors are in operation including life expectancy, the age of parents at childbirth, and immigration.
For a useful collection of authoritative facts and projections, I suggest http://www.npg.org/facts.htm.
The U.S. has less than 1/20 of the world's population, yet produces 1/4 of the world's greenhouse gasses. If countries such as India are to grow to U.S. style affluence, their energy use, greenhouse gas production, and many other environmental factors would become catastrophic.
It is not possible for the world to be remade in the image of Hong Kong. The needs of land for agricultural uses and waste disposal alone would not permit it (not to mention saving some space for wild species and natural recycling).
Meanwhile, we could solve almost all of the world's environmental problems simply by voluntary population reduction if it was promoted, instead of discouraged, by people such as Dinesh D'Souza. His misinformation is counterproductive and dangerous.