Your presenter is obviously wrong.

The US ans Europe with far smaller populations have significantly greater climate footprints than China and India, for example. And that’s before we adjust for the fact that a lot of China’s footprint is US/European footprint outsourced to China.

Indians having fewer kids will do nothing to reduce the already too large impact of the existing US/European populations.

Also the idea that women empowerment will help with reducing kids is decades old. If your audience was surprised by this, then they are clearly not well versed in any related topics.