The "why" is that it is a unique number for each of us that can easily get lots more information about us.

I remember in my distant youth that it was illegal to ask for it. I even remember the law: The Privacy Act of 1974. But everyone seems to ignore it. Or maybe it was rescinded without my noticing. In AZ they want it for your driver's license, but it is labeled "optional". And my insurance ID hasn't been my SS# for a long time (so I don't give it to doctors, either). When I first started working, it was. But that stopped 25 years ago. Even 1poorMIL's Medicare assigned a random number rather than using her SS# on her card.

FWIW, I never give my SS# except for taxes (I'm not messing with the IRS). But that doesn't really matter, apparently, because one entity I refused to give it ended up finding it anyway (I don't know how).