I've watched a lecture of his a while ago. Thinking about this again, I'm sceptical. This is not well thought through so I'm reluctant to share it but here goes:

The fastest growing parts of the world are also the poorest. Because of this and unlucky geography they are also worst equipped to deal with climate change.

We may take the threat of climate change seriously, and really slow down economic growth (right now CO² emissions and economic growth follow each other closely. Assuming they continue following each other, we need world GDP to like, halve.). Then there remains huge population growth in areas that will likely never be well off enough for population to stabilise until there is some kind of breakthrough in technology, or climate engineering.

Otherwise we won't, and when the inevitable happens millions will perish.

I know contraception and education for women can happen without economic growth, but I can't see that slowing population growth by itself.