If there is something in society that causes women not to want to have kids and this remains in place then the prediction is correct.
This is a nature versus nurture debate.
Your interesting and pertinent question has both an easy answer and a hard answer. I'll provide references for both.
The easy answer is that this behavior is "heritable," that is that correlations in rank order on this dimension of behavior are stronger for close relatives than for persons who are not close relatives. That is true of ALL human behaviorial characteristics, without exception. A genetically sensitive study design on any human behavioral characteristic from political behavior (who is "conservative" and who is "liberal") to obesity to IQ will always show a broad heritability greater than 0 (and always strictly less than 1). Everything that people do is heritable.
The hard answer is that even if a human behavior is shown to be heritable, as all human behaviors are, it still remains unknown how much the behavior is subject to environmental influences. Some human behavioral characteristics with high observed heritabilities are nonetheless highly sensitive to environmental influences. Most human behavioral characteristics are polygenic, that is they are influenced by many genes, each with a small effect, and even monozygotic twins are consistently found to differ in highly heritable characteristics, for environmental reasons that are sometimes still quite poorly understood. Knowing the heritability of a human behavioral characteristic says nothing about how much that characteristic is subject to environmental influences.
Here are the references I promised, recent papers by world-famous behavioral geneticists:
http://people.virginia.edu/~ent3c/papers2/Articles%20for%20O...
http://people.virginia.edu/~ent3c/papers2/Articles%20for%20O...
To sum up, in the context of this thread, a LONG-TERM trend of women having fewer children might be expected to reduce the reproduction most of women who have some genetic propensity to disfavor having children. But all women of all shuffles of the genes respond to societal and individual incentives to have more or fewer children, with few of those incentives yet being well understood. It is certainly possible in principle to reduce the trend toward reduced reproduction, irrespective of which persons (with which genomes) are reproducing.