>> ...giving it to the Indian government which ( at least theoretically ) have the responsibility to defend my interests.

That's an assumption not borne out by facts. The Indian govt. has denied that citizens even have a right to privacy [1]. And there is no recourse (or even disclosure requirements) if a citizen's data is lost, stolen or misused under the Aadhaar ID system [2].

This is not say Aadhaar or the Indian govt. are bad, but I'm just contesting your point Indians "should not be so uneasy" about giving up their biometrics and other data to the govt. There are massive, valid concerns.

[1] - http://timesofindia.indiatimes.com/india/No-fundamental-righ...

[2] - http://indianexpress.com/article/opinion/columns/aadhaar-bil...