Back when Social Security was first being put in place, there was a lot of concern that SSN's would become a "national Identification Number", and there were laws put in place to prevent this. However, said laws were largely ignored and SSN was pretty frequently used for all kinds of non-governmental purposes. In the last decade or so, there has been a renewed concern about SSN due to identity theft, and PII or Personally Identifying Information. It's now highly discouraged for anyone to store SSN numbers, although they can be still be collected for certain things like opening bank accounts and what not to prove citizenship, as well as to report to the IRS.
IMO the IRS should not be using SSN's for identification. But i'm not sure what else they can use.
The problem here is that historically, bug reporting was linked to tech support because only enterprise customers were expected to report bugs, and those customers were paying for those bugs to be resolved (hotfixes, for instance).
Nowadays, Microsoft is asking for bug reports from everyone, but has not fully created a support structure to make that feasible at scale. They seem to be iterating over the problem though, and maybe eventually they'll get it right.
I don't really have a pony in this race, but logically, there is a difference. There are strict government laws in place to protect SSN information, such laws do not exist (apparently) in India regarding Aadhar. I don't think the argument is (mostly) about having a national ID, but about the lack of privacy of that information. Of course biometrics are bad in another way... If one needed to, you could change an ID number, you can't change your fingerprints
IMO the IRS should not be using SSN's for identification. But i'm not sure what else they can use.