I like how we phrase this as “better education” and “better career opportunities for women”. While technically true relative to poor countries, these explain nothing about why fertility rates are so low. They are related, but framing them differently will help us understand.
Why do people have fewer kids? Because economic life in most developed countries is relatively unstable, and to ensure economic stability, we require people to develop years of education and work experience to receive a comfortable salary. In many places we now require two such incomes. This mean women really don’t have a choice but to pursue advanced education and work, whether they want to or not. And we are not willing to accommodate children during education or work. This means women (and increasingly men too) are severely penalized economically for having children, and so of course people will have far fewer on average.
Another likely factor is the atomized nature of the modern family. Many people need to move to distant places for work, severing their direct ties to family and community. Human mothers aren’t well equipped to raise children solo, and even two parents is a stretch if you have 2+ kids. In past times we always relied on neighbors and extended family to help keep an eye on the youngsters and to teach parents the skills they need to do it right.
If you look at the very wealthy, there is some evidence that they have higher fertility, though I couldn’t find good data on this so take it with a grain of salt. But they have access to enough money to buy personalized childcare, which solves almost all of the above issues.
In developing countries, children often mean free labor and form the basis of your retirement through elder care, so while the economic conditions are of course worse overall, the opposite incentives exist. Another factor is that poor, agricultural societies are almost always extremely patriarchal, which tends to lead to high (involuntary) fertility.
In my view, egalitarian economic reforms will help bring fertility rates in all countries towards a healthy moderate level.