Social Security is touted as an "insurance" program, but it is nothing of the sort.
Insurance, in and of itself, is risk management. You pay a premium, derived from the level of risk you are willing to assume, it's potential costs, and its statistical likelihood, so that if the "bad" thing happens, you have some or all of those expenses paid.
It doesn't matter who runs the program, whether profit or non profit, whether commercial or a mutual aid society, which is where almost all insurance programs started, such as the Amish continue to do now.
However there are two, very important, differences between insurance and SS.
First is that SS has no actual assets to draw against for paying out "claims." Every penny collected in SS taxes is immediately spent. For most of its existence, the surplus was immediately mingled with all other general funds, with nothing but a set of almost hidden bookkeeping entries made. It's not even counted as part of the government debt. There is no fund set aside to pay claims. Even mutual aid societies have, and have always had, those.
Second is that you have no legal right to any payout, even if you meet all the conditions under which you, mistakenly, thought "entitles" you to them. The government uses the word "entitlements," but, as far as government goes, there's no such animal. It's nothing but political shorthand to make it sound better. It stands for a class of benefits that is on "autopilot" as far as budgeting is concerned. Congress passes "rules," the administration implements the "rules," and they aren't affected by passing budgets ... except when Congress changes the "rules," which they are legally free to do at any time.
SS is a Ponzi scheme and always has been. Money paid out today is taken from monies collected today by an ever increasing number of "investors," with government grabbing everything "extra," just as Charles Ponzi himself did. Or at least it was until demographics started running up against the hard limit of available new people to fleece. For most of its existence, there were far more people paying in than those collecting. The retirees up until the last 20 or 30 years, reaped a huge bonanza over what they actually paid in.
These days, you don't even get out what you put in.
Government was able to spend far more money than they took in in regular taxes. When that "extra" money started drying up is when the budget deficits and the total debt started exploding. Politicians, as politicians are wont to do, just kept kicking that can down the road, initially knowing, and recently hoping, that they would be ready to retire before the time finally came to pay that piper.
That time is here.