It is known that as countries get richer, they tend to have less kids. Maybe it is because they are too focused on work for them, or maybe just less worried about more of them dying.

You should care about climate change because it is a huge threat to everyone.

You didn't say why you are so worried about population growth, but a lot of the reasons (actually, all the reasons) I see to worry about it are intertwined with climate change. More people existing often means more people ruining the environment, exacerbating climate change, and both more people and climate change make it harder to feed everyone. I don't see the dichotomy here, but maybe you have different reasons to worry about it?