Grossly, south korean couples each makes 1 child. So its population is going 1/2. To correct that and return to previous level, every couple formed among those children would have to bear 4 children.
Why do you assume the current population is the correct one? There’s a reasonable argument to be made that humans are over the Earth’s carrying capacity nearly everywhere, and are causing environmental and social damage to maintain the current size. It is quite normal in ecology to see crashes and recovery in the event of overpopulation. If we assume humans are biological organisms, it all seems pretty normal.
Except unlike the foxes which eat their rabbits to near extinction, and therefore soon join them, humans can change the rules of the system they're in.
Calculating the carrying capacity of the world before agriculture would have given you a much different number than after it.
Okay, sure, but none of that changes what I wrote. Past performance is no guarantee of future results. Nor that improvements to Earth’s habitability will be timely, nor whether incentive structures will line up to implement the changes needed.
My scenario is several orders of magnitude more common than yours. It doesn’t mean you’re wrong; miracles do happen. It must be nice to have so much blind faith in technological progress and human exceptionalism, but I’m going to stay with my ecology and statistics.
It's several orders of magnitude more common in species which have orders of magnitude less ability to impact their environment and change the way they live (and to humans in the past when we were no different).
It is not blind faith to say that we should expect that the different dynamics could be different when the rules of the game are different.
Again, if the foxes see the rabbit population declining and can start producing rabbit substitute before they start starving, of course we would expect a different dynamic to be possible.
Except that humans are now in a situation where modern medicine has also allowed us to live much longer. The natural cycle of birth-aging-death has been disrupted. You suddenly have a world where there are too many 80 year olds and not enough 8 year olds.
Grossly, south korean couples each makes 1 child. So its population is going 1/2. To correct that and return to previous level, every couple formed among those children would have to bear 4 children.
I think they won't and it looks grim.