As soon as that happens, the reproduction rate falls below the replacement rate.
The problem is that global society is actually not ready for a population that shrinks instead of grows. Many of our institutions are effectively pyramid schemes that rely on more people entering the bottom and paying for them than pull out money and exit from the top.
(Side note: I believe China is actually falling. There have been significant programs attempting to get women to have more children. Between education and "one child" (which is no longer in force) China has some demographic issues ahead.)
Women also need reproductive rights -- something that just took a hit in the US -- and the ability to support themselves. I'm not remembering/finding the rest of that list of 4 or 5 items.
Since men are physically more powerful, you also need a society with laws and people that will protect women and women’s rights. Women’s rights to mate with who they want, when they want, how they want, and earn income and be financially independent to be able to make those decisions independently.
To enlighten yourself, consider reading Federici's "Revolution at Point Zero" and Freire's "Pedagogy of the Oppressed."
What is it, I ask you, that makes a population difficult to oppress?
Second, a woman with a PhD would have more opportunities to avoid marrying you.
Why would we need to reduce world population?