Trying to justify the right of privacy is like trying to justify any other human right. They are called rights, not because you need to justify them, but because we came to a consensus that they are integral parts of a working society. The right to privacy is like the right to not being harmed, your right to free speech or right to freedom. All of these are nothing you need to justify in order to acquire them, you innately have them, period.
You may choose not to use them, but you can never use that as grounds to deny them to others. The answer “because I have a right to privacy” is enough to satisfyingly answer the “I have nothing to hide” paradigm; no justification needed for making use of basic human rights.