People talk about 'natural resources' and about how we're overpopulated all the time, but don't often want to go into real specifics. My guess is the repressed desire for death and depopulation came first, and the narrative later.

English-speaking culture is steeped in Christianity (even modern 'wokeism' is just another, more radical iteration of calvinism), and Christianity is a doomsday cult; we're fascinated by doomsday narratives, the end of the world, mass death- we're in love with these stories; look at zombie movies etc. The overpopulation meme is certainly going to be partially fed by how appealing 'the end of days' is to the western mind.

(Right wingers have a doomsday narrative, too, it's just a biosocial one rather than an ecological/geographic one; modern technology and the resulting societal shifts lead to selection against intelligence, and societal decay propagates irreversibly, leading to a future of stupid, lazy, and most importantly small-souled bugmen.)