My thoughts when confronted with "we have a finite planet with finite resources" is more "why don't we expand beyond the earth?" rather than "We have to limit the number of children people can have". So, why don't we?
I remember some discussion of this in Kim Stanley Robinson's "Green Mars", IIRC: he points out that it's simply too energy-inefficient to ship a few billion human beings out of Earth's gravity well, and no extraterrestrial habitat will have an ecosphere anything the size of Earth's.
Earth is simply the best place to support humans in the galaxy, and it needs to be sustainable in its own terms. We can and should live elsewhere, but that doesn't mean Earth will be any less important to us.
Yeah, I doubt someone with a sustainable habitat on Mars, and enough resources to send some back to Earth, is going to just send them without getting paid more than it would take to claw them out of the ground on Earth in the first place. It would make more sense to just keep the resources on Mars where one can use them, rather than wasting 95% of them transporting 4% to Earth.
Establishing sustainable colonies off Earth would put some of our metaphorical eggs in another basket, and make it more likely that our species could survive a major catastrophe. It's something we should be able to do in the next few decades or centuries, and I'm all for it.
But given current or reasonably foreseeable technology, we're just not going to be able to ship off enough people to relieve population pressures on Earth.
(Question: Has emigration to North America ever made a significant dent in population pressures in Europe, Asia, or Africa?)
