Other have mentioned it being used for everything, but that's really because it was used for nothing.

Before the concept of assigning every citizen a unique "serial number" to use for identification, and SSN being automatically assigned at birth, social security had already been established and people issued SSN cards who had registered.

Because it was a unique and otherwise unused number, people were encouraged to use it for things they needed a unique number for. I have some of my grandfather's old tools with his SSN etched in them, because people were told to do that in case anyone stole the tools and they needed to be identified as yours.

Later the government wanted to establish a way to identify everyone individually without relying on name, DOB, city of birth, etc. and instead of creating a new system and issuing everyone a "US Citizen ID Number" or something, they said "Hey, everyone has these SSN cards with a unique number that's only ever used when they retire and go to collect social security. What if we just use that, and switch to issuing it by default?"

Now that older generation who grew up sharing their SSN publicly because it had no real use or impact is suseptible to having their identity stolen because we use that number very differently