Still many countries are >2 but they're falling rapidly too. Its surprising to me to see Bangladesh at 2.1 and India at 2.2.
Places like S Korea 1.1, Italy 1.3, Japan 1.4 you can do the math yourself. (1.3/2)^N means without immigration their populations nearly disappear in 100 years.
Russia 1.6, China 1.6, Thailand 1.5 takes maybe 12 generations to do the same.
I looked at this source https://ourworldindata.org/fertility-rate which seems to imply that globally the number of children per woman is 2.5 so still much higher than the replacement rate (of course we'd have to talk about more than fertility rate to have a real discussion).
As far as I understand the projections about population stabilization are based on predictions of a reduction of children per woman in countries where this is still very high. It's possible that these predictions are right but they are just that, predictions.
As an aside, I think we should dedicate a bit more effort to try to understand the implications of both possibilities and a bit less to try to assert as certain what is just a prediction.
This is not obviously not only a reply to the parent's point, I just found myself writing a longer reply than expected ;)
For example. Let's say that while the majority of the population (Population A) is reducing its fertility rate a subpopulation (Population B) keeps it at a higher rate. Let's suppose that both populations maintain this behavior for several generations. In this case we would see an initial reduction in fertility rate not leading to a stabilization of the population
Will this happen?, I don't know. What I'm saying is that I feel in these discussions often people place too much faith on their preferred extrapolations ;)