He's not wrong in that belief. The issue is how to fix the problem.
Personally I'm OK with a plague (a real one next time please) or a meteor strike in a major metropolitan area or 2 or 6.
Population levels will take care of itself if humanity stops interfering in and funding third world growth.
Look at the first world nations with plummeting birth rates. It can happen "naturally".
I think there is a Goldilocks point where societies/cultures are successful at the survival game and breed at replacement levels without overrunning and destroying their environment.
Eventually though the society becomes so rich and affluent that it forgets what got them there and starts acting like it can reverse the laws of nature and natures God.
It is a balancing act.
There is going to be a big population crash at some point, hopefully I won't be here to see it because it will be horrifying, even if I'm not directly impacted.
You didn't say war. That's how
communists governments generally take care of excess inventory of their humans. It also has the side benefit of getting rid of a lot of the alpha males and others who might start vying for power.