The catch is population momentum, which explains why even with lower birth rates the world population will still rise to 9 to 11 billion.
With a biocapacity of around 12 billion hectares, the same population can manage with a footprint of less than two global hectares per capita, which is equivalent to what takes place in several poor countries.
However, the same population relies on a global economy that’s capitalist and competitive, which means it needs ever-increasing use of resources to support middle class conveniences, and then earn from that while maximizing profits. That means resource use far higher than what is sustainable.
Meanwhile, the waste generated from such activity may lower biocapacity through soil erosion, polluted water, air pollution, etc. Any attempts to clean up has an energy cost plus requires more regulation and coordination, things which work against free market capitalism.
From what I remember, the Church acknowledges all of these points, which is why it continues to call for population control and more regulation of capitalist systems. However, it does not support artificial contraception and abortion, and wants regulation to be done in a non-violent manner.