Overpopulation is certainly a general concern, and I doubt I will have children, have little interest in them, but I do like children and recognize that it is fundamentally important to our species that we continue to have them.
That is, the simplest, fundamental, inarguable framework of Biology. I am a Biologist, so, there I stand.
But why is that something that always takes care of itself?
Easy. Understanding how population systems work, in all known models of life on this planet (yes, all of them), no population of living organism can be modeled as a logorithmic growth system. It's just, mathematically impossible. Explosions can happen that way, briefly for sure, but no living organism can sustain that. Resources are not infinite. And they are shared. ...which adds to the difficulty of their not-infiniti....ness. See where I'm going with this?
The planet would determine our end, or we will, or there will be a pleasant mix of this, including the obnoxiously-possible chance that random cosmic acts could also, indeed, spell our doom, so all the good we can and likely will do--increased agricultural efficiency, addressing overall resource sustainment/waste-production (major factor of that climate change thing), to a point that we can add a nice mix of workable social policies that promote a real paradigm shift in structural, social systems where we have real societal shifts in understanding our actual personal responsibilities within the world, and doing something about it....we are still going to face the inevitablle, geologic, natural order of things as it comes to life-sustainment: we will run out of actual space. We just will. Yes, it could manage to be 10s of thousands of years from now...maybe more, quite possibly sooner though...much much sooner.
Hell, we're only about 200k years (Cro Magnon--so actual Homo sapien) of our life story. (austrolopithecine--aka Lucy--so I think still the first real "us," still living in trees, but doing some field-hopping and only eating nuts and grubs--was about 3.2 million ya?)....that's a geologic fart whistle in life stories. The Dinosaurs wrecked-face, all on their own, for like 100 million+ years! 100 million! (I think it was way more, actually)....then there was another dinosaur-era-length of time (76ish million years ago), before we fricking showed up! ALl the birds and chickens and shrews and sloths and such were kicking ass in all those years. Kicking ASS!
Of course...are we capable of managing ourselves with that sort of efficiency, after having eliminated some 99% of our actual evolutionary checks, that no other animal has ever erased (disease, predators, injury, foraging/hunting food strategies, etc etc etc)...added to a thoroughly-informed desire and need to draw up even more sustaining energy and lifeblood from the same planet? hahahaha, no. No, we would never possibly live that long.
For all of those reasons, and our tendency towards violence and brainless self-destructive competition needs (Actually, one of those self-population checks that we never seemed to eliminate, so at least we have that going for us).
So yeah, there are a great many reasons we can keep this train going for thousands and thousands of more generations, even by not doing the absolute horrendously stupid thinking of "not making Children" (you could always ask the Shakers how that worked for them. Oh wait...you can't), the type of problem that you present, while actually very real, remains outside the scope of our own social structures for self-preservation, and are determined by Biological Law, which basically works on a geologic scale. That's important to think about (and yeah--the potential for space exploration is part of what can keep us going for so long and, yes, potentially eliminate that Biological Law. Eliminate it. It might be one of the very last that we can eliminate...but anyway, that's something else).
Yeah, I dunno. That's how I think, lol. I tend to think about these things on geologic scales, because I kinda have to. (Evolutionary genetics spends a lot of time in the 3-200 mya time frames, just based on lab samples that we can obtain--you know, current species that can be traced back that far...unlike us--so it's the time frame where I spend a lot of my brain-thinking)
TLDR: This is actually a very good question, that is very difficult, and very complicated, but thankfully has one possible answer that is also very very simple: Regardless of whatever natural or social problems a population group or species faces at any given time in its life history, there is but only one fundamental, quantifiable variable that will insure the end of that population: failure to reproduce and thus replace founder generations.