Our economy and support systems are based upon growth. This includes population growth.
For instance, if there are too few people to generate revenue and service to support those in the society dependent on that revenue/service, the system will collapse. Think Social Security.
Social security as you mentioned is a good example. We only have that issue with our current social security system because we spend the money people pay in to social security as part of the governments yearly budget and pay out money to current SS recipients from the same yearly budget. This only works if there always more people paying money in than receiving it. We built a broken system that depends on continuous growth instead of just saving some of the money to distribute later. Making more babies is just bailing out water until it happens again with the problem only getting worse with each iteration.
Another huge issue that Elon never mentions or is not aware of is the coming robotics revolution. We are on the cusp of Industrial Revolution 2.0 with robotics. Robots will replace humans in the majority of jobs. Workers will shift to building and maintaining the machinery rather than doing the actual work. This requires less people but ones with higher skills and that's what we should be concentrating on, building an educated and skilled work force instead of just making more workers for jobs that soon won't exist.
But I'd say that the elephant in the room that not even Elon can dive into too deeply is that the real issue is WHICH populations are declining. Nobody would voice any concern if suddenly Japanese people started humping like bunnies and their population was set to reach a billion in XX years.
The issue is that productive and educated people are not reproducing as much.
Unproductive and uneducated people with their hands out for aid are reproducing a lot.
The problem is that only one of these groups has a chance to get humanity to the stars.
The question here would be "is focusing on maintaining growth the best/most sensible approach?". We see it in the economy all the time—companies go to incredible lengths, and often end up engaging in deceptive, immoral, monopolistic, and predatory practices, in order to keep growing. When their numbers show that they're not growing they freak out, investors panic, and sometimes end up in a death spiral as a result.
In a world where resources are finite, the room to grow is also finite. Now, I've seen arguments to the effect that our current supply of resources, if well managed, would be able to sustain the current population without issues. That very well might be true, but I suspect our current systems are not at all suited for sustaining continuous, endless growth.
The cracks are already very visible in our current systems, I think. And I'd argue that there is a positive feedback loop in effect already when it comes to population decline—the system expects you to generate wealth and growth to sustain it, but you get less and less in return, which affects your ability and/or desire to contribute to increasing the population and taking on additional responsibilities and costs. This, in turn, leads to the system demanding more from the existing population, further impacting their ability/desire to reproduce, and so on.
I don't want to fall into the "rich people bad" meme, but it's much easier to worry about population decline when the existing socioeconomic structures are already in your favour.
Current prediction is that world population will continue to grow till at least 2100 and will peak at about ten billion (https://www.un.org/development/desa/pd/content/World-Populat...)
It may or may not collapse after that, but that’s far out. Global warming, IMO, is a much bigger threat.
An aging population may become somewhat of an issue, but that’s solvable by migration, at least for the richest parts of the world (lots of young people already emigrate to the USA and Western Europe, sometimes leaving behind an aging population)