Where did this right come from? and since when is this a thing? Don't mean to be condescending but "the right to privacy" isn't really a thing in this particular domain (legally speaking)
I can't pretend to do justice to the long history of the concept, but we can at least say that for the latter, privacy has been considered an important human right since at least the UN declaration of 1948. This has been carried over into European law, see all the iterations on EU data protection laws. The UN statement is Article 12: "No one shall be subjected to arbitrary interference with his privacy, family, home or correspondence, nor to attacks upon his honour and reputation. Everyone has the right to the protection of the law against such interference or attacks."
For the US, this dimension of human rights did not deeply inform policy. Here discussion around a "right to privacy" really began in a different context with Brandeis and a right to be "left alone", largely meaning from the press. Many of the cases that inform privacy law in the US are oriented towards such scenarios and do not necessarily translate well to the context of data. See http://groups.csail.mit.edu/mac/classes/6.805/articles/priva.... There is rather a discussion on the accuracy of financial data about a person that stems from credit reporting.
The other area that would have to be discussed is of course wire-tapping laws, but leave that for another day... In sum, the question of a "right to privacy" has a long tangled history even just within the West, but is decidedly a thing in the EU.
I think we should fight for it because I think it makes life better and because I don't want to live under an oppressive government.
The idea of basing our sense of right on what is law, rather than basing the laws we write on our sense of right seems to be bafflingly common.
Another archaic concept, I fear, most days.
In my mind:
ethics = definition of what improves the common weal
law (should)= enforcement of said ethics