if people stop having children, it breaks the system

The overriding fear I've seen is that not enough white children are being born. And as the definition and context of whiteness shifts, this inspires varying degrees of alarm and hatred. A big part of the current Israel/Palestine conflict stems from the demographically older and more infertile Israelis believing they need to cap the younger and more virile Palestinian population by any means necessary (including the current genocide).

So it isn't even that "people stop having children", but the "right" people not having the "correct" kind of children.

we better go full speed ahead on a the most moronically large scale sunk cost calamity that is going to hit us like a brick wall

Sort of the dirty secret about climate change is that its got nothing to do with population size. Enormous amounts of natural resources and carbon emissions are being produced by vanishingly small portions of the population. The whole AI project has been a fossil fuel hog. The wars in Iraq and Afghanistan consumed phenomenal volumes of material for the benefit of an infinitesimal sliver of the planet's residents. Reliance on disposable plastics and love of enormous cars has nothing to do with the number of children we've been having.

Anti-natalism is completely divorced from ecological sustainability. In many ways, it is rooted in this delusion that we're all living in these remote rural settings with an infinite frontier to exploit forever. And that mentality emerges most forcefully in places that don't have these dense urban populations.