"It is no use appealing to advances in agricultural science-'green revolutions' and the like. Increases in food production may temporarily alleviate the problem, but it is mathematically certain that they cannot be a long-term solution; indeed, like the medical advances that have precipitated the crisis, they may well make the problem worse by speeding up the rate of the population expansion." (Page 111)
Our world is unable to withstand continued population growth & continued agricultural expansion. We will simply run out of resources, and it will lead to deaths on a mass scale. It makes sense that in many places the birth rate is falling.
Given the world we live in and how aware many of us are that we are running out of resources, it is no doubt that many people are deciding not to have kids. As well it is a fact of life that the birth rate tends to fall in first world countries, as the child mortality rate lowers, the number of children people tend to have lowers. This combined with economic and social factors around having children, education for women, people getting married later in life, etc. It is no surprise that in many places the birth rates are falling.
Global population growth is declining, it peaked in 1963 at ~2.2% according to the UN.