There could also be an economic explanation. Traditionally large families were favored because they provided old-age security to parents. If an immigrant from a developing country is able to support their parents with remittances from a developed country, then there is less of a need for large families in the developing country.
Were they? If we asked old women why they had 3, 4, 5+ kids, would they say it was so they would have old age security or were they having them because they did not have a choice to not have them?
There's a reason why Pushkin had 4 children by the time he got shot, the man was no fool to do that accidentally.
Societal pressure may exist but, since society consists of men and women, you still need to explain their motivation. To me, it is a mystery-ish.
It is not that the men wanted or did not want kids, they could not have cared less. Or they could have wanted them as assets, at least the boys. Either way, I doubt too many were sufficiently fussed about the woman’s sacrifices, especially if it meant they had to completely give up sex.
We went from it being common to see women having 5 kids to it being rare within 1 to 2 generations. I would bet on it being due to women gaining true independence.
Edit: just to be clear, I am not condoning that. Only thinking about possible motivations.