Also neither is yourself getting children or other people getting some a guarantee for a dignified existence in a future nursery home nor is such utilitarian thinking a good basis for deciding on whether or not to bring someone into the world.
Humans will eventually go the way of the Dodo - and that's okay. Because we are not special. Not at all.
I remember visiting for the first time my great grandmother when I was 6 years old. She was 99. When she saw her great grandson topless with shorts (hey it was the tropics) she reached forward and gave me a massive purple nurple and laughed. She was still shopping daily and moving around.
So I'm not really sure what scare mongering tactics in favour of parenting you are trying to propagate here.
Don't have kids just because you are expecting them to take care of you in old age. That's just cruel.
Here is a better reason: You'll be dead quite soon in any case, so unless you're in agony, you may as well enjoy your final days here. Think of some of your favorite activities and pick one. Rinse and repeat.
Sound shallow? Maybe, but I've spent an awful lot of time contemplating the question.
In the future when people have real options this is less likely to be an issue.
At a societal level, is an imbalanced population pyramid a problem? Yes, and many countries are solving this by opening up immigration options.
Should an individual opting not to have children be expected to have negative consequences in old age? IMHO, no.
Unless they are getting immigrants from off world, that is at best a game of musical chairs. Birth rates are plummeting globally.
Sure, you can still find nice big numbers in places like Niger in sub-saharan Africa, but even they are starting a sharp decline. And they are starting with a low base. Their entire national population is only the size of the greater NYC area.
People often say you shouldn't have kids for your own retirement. In the ultimately hypocrisy, they often mean kids will be for everybody's retirement (when they're forced to pay social security taxes as adults).
The economic incentive is to let others have kids and shoulder disproportionately the costs, while you can free ride and "not have negative consequences." Immigration doesn't solve this problem at the system level as removing children from foreign tax pool into our domestic pool shifts benefits from one elderly person to another.
The question is then who will care for these people when they get old? Other people's children? So other people should have children, put the effort to raise and educate them for your benefit? This is a very egotistic view.
The modern retirement system is merely an additional layer of indirection over the traditional system of kids taking care of their elderly parents.
If later they learn something unpleasant about nursing homes, or pension plans, or something else relevant to their expected quality of life at their old age, then that might tip the scale towards having children, even though it is only one of many reasons.
The last reason that tipped the scales towards a decision is not necessarily the only one or even the most important.
Similarly, if I go into vegetative state I hope someone will use my organs for some good cause, not try to keep me alive by any way possible.
If your answer is that you are not planning on counting on it for the future then a lot of people will ask why not stop paying into it and keep the money taxed for yourself? It is a significant tax. You CAN actually stop paying into it and then make yourself ineligible for payments out which includes spousal benefits being cancelled. You CAN conscientiously object, it is a provision of the SSA law.
If a lot of young people saw that, they would withdraw from it and put the trust right now into a deficit which would adversely affect the people withdrawing from it right now.
I think there is a non zero probability of this happening regardless for different, uglier political reasons but it doesn't make a lot of sense for people to be forced to pay into something with no promise of ever getting something back.