What a ridiculous false dichotomy. Earth has a huge (and increasing) number of humans on it. We are in far greater danger from unsustainable depletion of natural resources than we are "dying off" from gradually declining birthrates.
I'm much more worried about climate change leading to war and famine than I am about women voluntarily choosing to have fewer children. As far as I can see, population decline is only a problem because our current economic system assumes endless growth.
In the meantime, our species has much more urgently pressing issues.
Fucking the environment is very unlikely to destroy humanity, and that is really the only concern of any species.
As conscientious pieces of a greater whole, however, there are definitely more pressing issues.
Why should that be scary?