The slowing down of population growth is real though. Trend of fewer children is across the board not just developed countries. Current trajectory estimates population to peak out in 2050-2080 and then decline, for some in their youth in next 30 or 50 years may not be that too far to completely dismiss.

Scroll down that page a bit and you'll find the "Rate of Growth" chart where you can see a clear decline in birth rate increase globally since the 1960s and it'll only be another decade or so with current trends before we are in genuine negative population growth. And that's also assuming there are no more pandemics and/or global scale ecologocial catastrophes likely to happen in that time (there almost certainly will be).

I think it's because we are living longer and the effects of lower birthrate will be shown later