What's the reasoning behind that? That doesn't seem at all obvious to me?
I would expect that the issue is, whether standard living that we collectively decide as a nation we want to have can be sustained from the wealth generated by the proportion of the population who are actually working. Provided that's the case, then in order to keep that income long term, you simply need each generation to be the same size as the previous generation. If the proportion of the population working isn't sufficient to do that, then you have a problem - but one whose answer probably lies in economics rather than population size.
Watching the video posted above, it appears that the ideal scenario is to have more working age people than children and retirees combined.
So let’s say in this hypothetical example that there is a society with exactly 10 citizens for each age, and everyone lives to their 100th birthday:
Age 90-100, retired (100 citizens)
Age 80-90, retired (100 citizens)
Age 70-80, retired (100 citizens)
Age 65-70, retired (50 citizens)
Age 60-65, working (50 citizens)
Age 50-60, working (100 citizens)
Age 40-50, working (100 citizens)
Age 30-40, working (100 citizens)
Age 20-30, working (100 citizens)
Age 15-20, working (50 citizens)
Age 10-15, not working (50 citizens)
Age 0-10, not working (100 citizens)
That gives a total of 1000 total citizens, of which there is a 50/50 split between economically active and inactive people. To increase the ratio to favour working people, you either need to increase the retirement age, reduce the age in which young people start working or reduce the age of death.
Or you could change the above table so that there are more citizens in economically active groups, but this is where it starts to get tricky:
Age 90-100, retired (50 citizens)
Age 80-90, retired (50 citizens)
Age 70-80, retired (100 citizens)
Age 65-70, retired (100 citizens)
Age 60-65, working (100 citizens)
Age 50-60, working (200 citizens)
Age 40-50, working (200 citizens)
Age 30-40, working (200 citizens)
Age 20-30, working (200 citizens)
Age 15-20, working (100 citizens)
Age 10-15, not working (100 citizens)
Age 0-10, not working (100 citizens)
With a total population now of 1500, you have nearly two thirds of working age, but the elephant in the room is the low number of children in proportion of working adults, assuming that these will become part of the future workforce.
You’ll also have to assume that for every citizen that dies, another one is born to keep the population at exactly the same level. Going by the second table, if everyone in the 30-40 age bracket had one child, the next two generations would consist of 200 citizens, but the two generations after that would only produce 100. Fast forward 40 years and the population will look something like this:
Age 90-100, retired (200 citizens)
Age 80-90, retired (200 citizens)
Age 70-80, retired (200 citizens)
Age 65-70, retired (100 citizens)
Age 60-65, working (100 citizens)
Age 50-60, working (200 citizens)
Age 40-50, working (100 citizens)
Age 30-40, working (200 citizens)
Age 20-30, working (200 citizens)
Age 15-20, working (100 citizens)
Age 10-15, not working (100 citizens)
Age 0-10, not working (100 citizens)
This creates a significantly larger elderly population, giving an even 50/50 split between economically active and inactive people. While that may not be alarming, it does show the importance of maintaining a stable birth rate without allowing it to spiral out of control.