There are many different demographic forecasts that predict the population of the world will begin to enter rapid decline. Those forecasts are likely

But extinction as a product of the failure of humans to reproduce is not likely. Instead, the endpoint is a much small more sustainable population.

Society will have to totally reorganize around these smaller numbers and changing mix (more seniors) in the populaiton.

A better way to look at population trends may be found in economic theory.

When demand for a product goes down, then the value of that product declines. Until supply begins to adjust. As supply drops its value increases and eventually reaches a new point of equilibrium.

For many countries around the world, the "demand" for labor has declined to the point, that cost of supplying that resource is no longer worth the investment so instead "parents" are "producing" fewer children but investing more heavily in their skills in order to differentiate their labor value from "generic" labor.

At some point, this will reach a point where labor become highly valued and at that point a new equilibrium will be reached.