His argument is akin to arguing that the Soviets lost WWII because they lost so many more soldiers than the Germans. But that's not what happened. The Germans might have had a higher score, but the Red Army still pushed them all the way back to Berlin and Hitler died in a bunker. Success is measured in achievements, not by lack of failure.
For the poor to stop breeding would be ceding their one and only competitive advantage. Humans, and for that matter, life on Earth in general, aren't "judged" (in the sense that extinction/flourishing is a judgment) based on how many failed organisms they produce. Rather, that determination is based on how many successful organisms are produced.
As residents of richer countries, we're conditioned to breed at or around the replacement level and to view each failure as a catastrophe. So when we see those 80 gum balls being added each year to his misery containers, we're viewing it through the lens of seeing the failure. But in poorer countries, people adapt to the increased chance of failure by having more kids. They breed well above the replacement level knowing that, in all likelihood, not all of those kids will succeed. From that perspective, you need to focus on that 1 or 2 gum balls being allowed into the richer countries. That's the success. And having fewer kids runs contrary to that goal.