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.

Yes, common objections are that the economy could crash or that humanity could go extinct. I don't think these are good objections, and I have different reasons. It seems like a bad "an end justifies the means" way of thinking sometimes.

Honestly, the economic crash one is weird. The logic is that we must sacrifice our present and immediate future (that happens to be millions of lives) so that other lives are better (supposedly). Huh? It reminds me of the argument I heard against prohibiting animals in circuses. They argue that the animals that were in the circuses at the time would be slaughtered or abandoned, so their logic was allowing more and more years of animals suffering inside the circuses. What? Yes, the change definitely hurt, but it was possible both to fight against their slaughter and abandonment, and to get rid of that abuse forever. If we decrease in population, of course it will be difficult, but we can find ways to face the difficulties while we get into a better system. We cannot preserve capitalism just because we are afraid of hard times, when capitalism itself is hurting us.

The extinction one is different. We won't get to that point, but even if we did, it would be a free decision of humanity that is hurting no one else. That's the intuition they probably have: that those humans would be hurting the ones that do not exist yet, but I already commented about that reasoning. I don't think there's harm against the non-existant. Our end is possibly inevitable because the habitable Universe seems to have an end. If we decide to fight it, that's okay as long as we do it ethically. But if we collectively decide to end it all, I respect it as long as it's done ethically too. Anyway, as I said, this is mere imagination as I do not see humanity (in the big numbers we now are) never ever choosing this path together. We will be here for some time.