I truly believe psychology is at the root of this. People start families when the optimism they feel about the future outweighs the pessimism. Even if this evaluation is done subconsciously.
At some point, in first-world society - averaging across different societies and social support systems, and considering the numbers in aggregate - we flipped. Pessimism about the future outweighs optimism. Downstream of that flip, the prevailing trend changed. Here we are.
Hard to believe that people who suffered the atrocities of the first half of the 20th Century were tremendously optimistic about the future, yet birthrates were MUCH higher across the world.