It's an argument based on false premises. Limitations on resources have, in past, proven to be fairly meaningless, and there's no particular reason to believe this will change going forward. Every time we think we've hit a wall(running out of wood in the 18th century, whales in the 19th century, food in the 20th century, or oil in the 21st century), we've come up with new technologies to keep going without much trouble(coal, oil, GMOs/agricultural chemistry, and tar sands/fracking respectively). Limitations on space are even less relevant.

Conversely, we've built first-world societies on a governmental safety net that only actually works with an increasing population. If we don't grow, then pension plans will start detonating like someone's carpet-bombing the economy. (Yes, worse than they are already). I think the people who created those pyramid schemes should be taken out behind the woodshed for a posthumous beatdown, but it's a bit late to fix it now.

If you want to know what a negative population growth rate looks like, look at what will happen to China over the next couple decades. It's the biggest demographic time bomb in human history.

Also, if you're bringing sustainability into this, IMO the only truly sustainable option is to advance technology so fast that we can defeat the Second Law somehow. Anything else just delays the inevitable.