Actually most advanced societies are not producing enough children to keep the population stable.

But they're importing enough immigrants to more than make up the difference.

Which is a very good thing.

Is it? Advanced society's dying off isn't something people usual celebrate.

Nobody said dying off, but it's a well-understood fact that humanity is growing at an unsustainable rate.

Good. There are too many people as it is. Running the birthrate at below replacement levels for a few generations is the only humane way to address that.

We're not well above carrying capacity for the environment, seeing as how mortality rates are going down and not up.

We're probably above sustainable carrying capacity. One of the great race conditions humanity faces is whether the bulk of the world will develop to a high enough standard of living for birth rates and hence population to drop before we run out of the natural resources we need to feed our current population.