I don't agree with the premise (data point: I grew up poor, with siblings), but certainly the inverse isn't true.

Singular data point. Were talking macro level.

Talking about the educated West where people have the information and tools to make the decision.

Context inference is important

Macro level poorer people have more children than middle class and up people. In the "educated west" (and elsewhere in the world as well I think).

extremely strong inverse co-orelation with education even in poor countries.

Exactly. I suspect the lack of understanding or overcomplicating the reason the birthrate is declining may have something to do with the much higher than average salary of the average HN commenter relative to the average worker's salary in the US. It's common for people who need to go to the doctor to avoid going to the doctor because they can't afford it. A baby is an order of magnitude more expensive than that and an ongoing expense of doctor visits and potential ER visits among other costs and logistical issues.