It says fertility isn't an issue today, but it's a little out of touch with today's anxieties; most of Europe and Japan have such low fertility that their native populations are in decline.
Their problem is not couples trying to conceive and failing, but people choosing not to have children.
Which does not prevent it from being a problem. Government policy can change that. Not forcing teenagers to go $150.000 in debt and to have a career to repay that until they're in their 30s would be the bare minimum.
But a fertile body can influence the mind in all sorts of ways -- changing hormones can modify sexual desire, for example.
In fact, global population will likely peak around 2050, and then start falling, which will be a whole new crisis. People will look back at overpopulation fears and laugh.
A rapid fall in population would be problematic, but a steady state or slow gradual decline would be beneficial - and perhaps environmentally necessary.
Obviously you need to ensure there are enough young people to support and care for the elderly, so population can't be too top-heavy. But improving technology (robots, AI) should reduce the need for labour without compromising living standards.
Like for example, look at this Haiti plot: https://knoema.com/atlas/Haiti/Population-density
It is already 1.5x more dense than Germany. 3x more dense than China. Would it stop? When?
Why is Switzerland 9x more dense than Ireland? Is population of Ireland expected to eventually grow to that of Switzerland?
Ironically, of course, the only workable solution to the demographic crises in Europe and Japan is immigration. Otherwise, pension responsibilities will overwhelm the working-age population and the whole society will collapse.
Staving off a demographic crisis using mass migration of middle class people from developing nations is a bit like staving off a petrochemical crisis by fracking or digging up national parks for coal. You're just shifting the problem to another time period and making irreversible changes to your country. It's not at all sustainable.
Global population will peak, so eventually every country will have to come to terms with an ageing population. In many ways, Japan is trail blazer here while the west has its head in the sand.