Birth rates certainly do plummet but I suspect, admittedly without having looked up the figures, that the effect has more to do with each couple having fewer children than with a substantial change in the number of people who choose not to have children at all.
People learn fast.
More seriously, a reduction in number per reproducing person is also evidence against the value of kids.
Imagine McDonald’s comes out with a new hamburger recipe replacing the previous hamburger, and marketing comes back telling you that total consumption has fallen 90%, that not only is your market share not growing any more, it’s actually shrinking, and something like a quarter of your customers no longer even eat a single hamburger, and the others are sufficiently disgusted that when they used to order 10 or as many as 15, now they only order 1 or 2 burgers.
Do you say that only the quarter matters, and the other customers who went from 10 to 1 says nothing about how delicious your new burger recipe is?
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