Overpopulation is nothing new. Back in the 1800s, a man by the name of Thomas Malthus saw that Great Britain's population was growing faster than ever. The reason for this is because of falling death rates. You see, for most of human history, mothers had many kids but many of them would die before reaching adulthood, primarily from disabilities and diseases. With the imporvement of healthcare and the arrival of vaccines, child mortality rates fell and the children who survived and ended up having children of their own, this naturally cause the population to grow faster. Overpopulation fearmongering is based on the idea that resources are limited and thus any population increase will reduce the number of resources per person. While resources are finite, innovation can allow for resources to be used more efficiently and for more resources to be discovered. Malthus was concerned that the growing population would increase poverty. He knew that prodution was increasing but beleived that it only increased linearly while population grew exponentially. In reality, production grew quicker than the population and poverty was lower at the end of the 19th century than at the beginning despite the population increasing by 60%.
In the 1960s, Paul Ehrlich predicted that a worldwide famine would take hold within 20 years due to overpopulation. He stated that there was no way that India could feed its growing population. the world population is twice as high as it was in the 60s and India's is triple, despite this, there were no worldwide famines and poverty actually fell (India currently hosts one of the world's fastest growing economies).
At the current rate of population growth, the population at the end of the 21st century will be close to 30 billion, but due to potential technologies such as desalination, GMOs, vertical farming, aquaculture, and cultured meat (a large percentage of our crops go towards feeding animals and thus artificial meat would save on resources), our ability to produce keeps going up.
However, the world population won't be anywhere near 30 billion because fertility rates are falling. You see, after the death rate falls, the birth rate also begins to fall. There are a few reasons for this. For one, with a guerantee that pretty much all of your kids will survive, the need to have many children goes down. Another is that having kids as a farmer is an asset while having them in an urban area is a liability (industrialization draws people to the cities). Other factors include increased access to birth control, more education (having kids later will naturally lead to less kids overall), and increased labor force participation from women. Eventually, the fertility rate will reach its final resting place as it has in most developed countries. The UN projects that the 2100 population will be 10-12 billion. And unless we discover immortality which triggers runaway growth of life expectancy, the population will remain roughly at that level.
