Fertility means "ability to have offspring", but the article says that the declining number of childbirths is mostly because of choice. I think we need a better word then.
Observe that the first thing wikipedia says in the entries for both topics is, "Not to be confused with" the other.
https://en.wikipedia.org/wiki/Total_fertility_rate https://en.wikipedia.org/wiki/Birth_rate
It turns out that while the dialects share roughly the same first definition ("(of animals and plants) the quality of being able to produce young or fruit:"), British English has a second definition: "(of land) the quality of producing a large number of good quality crops".
In that sense, I can see why they used the word. They sort of invented a new definition, "the quality of producing a large number of good quality humans."
https://dictionary.cambridge.org/us/dictionary/english/ferti...
Edit: Looks like I've been missing the story on this one.
Interesting that the articles all talk about obesity, unknown chemicals, brief style underwear, and whatnot as a possible cause without stopping to consider that maybe societal attitudes towards masturbation may play a role.
https://www.vox.com/science-and-health/2018/9/17/17841518/lo...
The takeaway: https://i.imgur.com/RhrrNI2.png