It's not only one cause - declining TFR has to do with a ton of different things, access to birth control being one of them but far from the only one.
You’re pointing out the mechanism. I’m talking about why people choose to not have children. This is not a disagreement.
The point of your parent comment is that the people in the developing world might also choose not to have children if they had realistic access to birth control - thus making the “why” incorrect. It could just be that having kids isn’t actually worth it.
I think this js the main reason. Most people here get children unplanned and the minority of them are rich.