It’s a total myth. Anyone who tells you otherwise either can’t do simple math or has an agenda to push. The replacement rate for an industrialized human society is 2.10. That means that in order to maintain its population, every woman in an industrialized society needs to give birth an average of 2.1 times in her lifetime (in non-industrialized societies the replacement rate ranges from 2.3-3.3 based on the local mortality rates, etc.). The replacement fertility rate for the world on a whole is 2.33, while its current actual fertility rate is about 2.45 (and has been steadily dropping). If a society maintains its replacement fertility rate, its growth will be zero and the population will remain stagnant. More than that and the population increases; less and it decreases. Anything beneath that and the population starts to shrink. Anything beneath 1.4 (if I remember right) and the society has reached an irreplaceable rate. In other words, there’s no hope of them recovering.
Here’s a link to a Wikipedia page providing various lists of fertility rates around the world from 2009, 2011 and 2013. Notice that over half the countries listed for 2013 were at or below the replacement rate for an industrialized nation, while 18 of them were beneath the unrecoverable rate, while several others are on the brink (and likely have fallen beneath it since the CIA’s list for 2013 was published). The only thing that had been keeping the US rate above 2.1 was immigrants from Latin America, but several reports came out over the last few months to indicate that the US fertility rate had dropped to anywhere from 1.99-2.06. One report I read stated that the global population will peak around 2050, after which we’ll start declining at a drastic rate, possibly as much as 1 billion per decade. The only thing keeping the numbers artificially high now is that life expectancy has increased by such a great degree.
With the political left promoting and forcing contraception and abortion on developing countries throughout the world, we’re seeing dropping fertility rates virtually everywhere. Europe’s population is expected to fall by 100 million by the end of the century, while Russia and China’s could drop by half. Japan, Greece, Italy and a couple dozen other nations are literally breeding (un-breeding? non-breeding?) their way to extinction. The bottom line is that, if you look at the facts as opposed to the propaganda, there’s no way you can buy into the overpopulation myth.