If you know the SSN and a few other personal details (like address and phone number), you are assumed to be that person, and can get access to their accounts and sign up for credit cards or loans over the phone or internet.
But every company that uses SSN to authenticate you also must store the SSN, it will be visible to their employees, and recently SSNs, addresses and many other details of most adult Americans got leaked in the Equifax hack.
If this sounds completely crazy and insecure, it is. An ID number should not be a password, it should be a public primary key. And some other method should be used to actually authenticate the person - one that does not ever require handing it over in plaintext.
When someone wants a loan or anything like that then we have to show our real ID card or passport, or authenticate on the web with our smartcard and pin. So nobody can do stuff that's possible in the us - apply for credit cards and loans without authenticating properly.
It identifies someone but it doesn't authentify him. Just like shireboy is your identity but it doesn't authentify you.