I guess I don't understand what's supposedly been proven wrong?

There seem to be real concerns about whether the environment on Earth can sustain the impact of human society in its current form, and the population is an obvious lever to scale that impact.

I guess what's "surprising" is that birth rates are responding to the pressures I'm alluding to? Rather than just continuing runaway exponential expansion?

I think people are talking about two different things. The initial panic was that agriculture could not scale to population growth, and millions would starve. That part turned out to be quite seriously wrong, the reason people starve is that they have really crappy governments.

The idea that a growing population has quite serious effects on the natural environment hasn't been proven wrong. Trying to get the entirety of the third world up to first world living conditions is putting a serious strain on natural systems. Having a lower population would probably help with that problem.

The current panic around falling populations seems to have two drivers: economic systems that are built as essentially a ponzi scheme, like many retirement plans including social security, and a pretty racist idea that we need to have a lot more white babies to keep brown people from taking over.