In the west, generally speaking, female employment and economic power has been rising and birth rates have been falling, except among religious minorities. David Friedman provides some explanations:
“Tetra Pak® – Housewife at the dairy counter in a Swedish shop” by Tetra Pak is licensed under CC BY-SA 2.0 
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One possible explanation is changes in norms and legal rules that make mate search more difficult. An example is a norm against dating fellow employees and a stronger norm against dating someone who has authority over you or you have some authority over.
For many people, their job is the only context in which they routinely interact with lots of other people, the best environment for mate search. The interaction often provides a way of evaluating someone for characteristics such as honesty and competence as well as compatibility, much harder to do in the context of dating, harder still in computer dating. It works better for people who not only are fellow employees but are actually working together, which often means one just above the other in the office hierarchy.
The same issue arises in the university context. Undergraduates are free to date each other — mate search is arguably one of the main functions of college. Junior faculty members, likely to be unmarried, are commonly not supposed to date students, even students not taking classes from them, certainly not students who are. I am not sure what current norms are for graduate student/undergraduate interaction, expect graduate student/faculty romance to be at least somewhat frowned upon, especially if the faculty member has some authority over the student which is likely if they are in the same field, the context in which they are most likely to get know each other.
Another cause for declining birth rates might be changing norms of courtship. I have not been part of that market for over forty years but I gather from what younger people say online that many men believe that making advances that do not turn out to be wanted is not only embarrassing but dangerous, that they risk being accused of harassment or some related offense. In the student context, many men believe that if a romantic partner changes her mind she can get him into a great deal of trouble by taking advantage of a college disciplinary process heavily biased against men. I do not know to what degree that belief is true but many men believe it is, which could be expected to discourage courtship.
Along related lines:
Also, when I was working for a big time international consulting firm, they tried to come out with a formal rule that said that you were allowed to ask out a co-worker, but only one time. If they said no, you could never ask again. Apparently the Italians howled with laughter and insisted that if this rule was enforced in Italy, no one would ever have kids, as the typical Italian courtship approach involves like a dozen rejections before ultimately the woman finally gives in. (GoneAnon)
That cannot be the full explanation since Italian birth rates are down too. Since birth rates are down in all or almost all developed countries and many less developed ones, it is worth investigating how widespread the relevant norms are.
Housewife Becoming a Low Status Profession
For a very long time, the default system for producing and rearing children was a married couple, with the husband producing income and the wife in charge of running the household and rearing the children. Over recent decades, the woman’s role in that division of labor has become a low status activity, lower status than making a living in the marketplace, much lower than professional success.1 Being an unmarried adult woman used to be, in most contexts, low status, on the presumption that if she could have caught a man she would have. At present, in much of western society, that has reversed — being a married housewife is lower status than being an employed single woman.
…arguments from the stay-at-home moms I know, who say people are constantly giving them grief about it, and who are often looking for some part-time make-work job they can take just so people will stop giving them grief about being a stay-at-home mother (Scott Alexander)
It is possible for a married woman to have both a job and children or for an unmarried woman to have children, but the former is more difficult than for a full time housewife, the latter much more difficult.
1. For a much more detailed presentation of this explanation, along with arguments against a variety of alternatives, see It’s embarrassing to be a stay-at-home mom.
