There's also this mindset that a significant decrease in global population due to some catastrophic event is both inevitable and has solid precedent. But it's not (at least not on historical, rather than evolutionary, timescales), and it doesn't.
When was the last time that a catastrophe caused global human population to fall by a significant fraction? When was the last time it fell far enough that it didn't recover all of the decline and more within a couple of years, much less a couple of generations?
55 million people died in the Great Chinese Famine of 1959-61. That was more than eight percent of the approximately 660,000,000 Chinese population at the end of 1958; By the end of 1961, the Chinese population had already recovered to its 1958 level.
The Blue Fever (now often called the 'Black Death') caused a world population decline that some place at as much as 20%; Population may have taken almost two hundred years, or seven to ten generations, to completely recover. That's the biggest catastrophic world population decline I am aware of, both as a proportion of total population, and in terms of time taken to recover. World population is estimated to have been about 450 million in 1340, and was 'only' around 375 million in 1400. That catastrophe could have been almost completely averted by antibiotics.
Exactly. So why the bejesus do you believe this:
Anyone who thinks population is going to grow beyond the next couple of decades hasn't paid attention since the 1970s
It doesn't matter if it CAN. Because it WON'T.
When fertility falls so far that the population starts to decline, say in 2050 or whenever it's currently projected to happen, what the heck makes you think that isn't going to be merely another temporary dip in the overall trend, another Great Leap Forward / Black Death?
The current drop in fertility is great for human happiness, but it's just another natural catastrophe from the gene-level point of view, and from the subculture meme point of view. Oh my god, something unprecedented in a billion years of evolution happened: a disease organism evolved a bioweapon that lets its hosts have sex without making babies, a billion years of optimization targeted at making organisms want sex as a proxy for wanting babies thereby rendered futile. The end result is predictable: our genes will evolve a countermeasure, in the unlikely event that some subculture meme complex capable of Lamarckian evolution doesn't beat them to it.
ETA:
Can we be sure the world's population will stop rising?