It really comes down to trust, or the lack thereof. People don’t trust their governments and governments don’t trust their people. I think this mistrust originates from governments so often being imposed on the people, rather than the government being subordinate to the people. If the government were truly subordinate to the people, I don’t think privacy would be nearly as much of a concern.

According to this the idea was coined even before WWI

https://en.wikipedia.org/wiki/Nothing_to_hide_argument

The origin of the quote is not Goebbels.

Someone else has traced the quotation to a novel by Upton Sinclair in The Profits of Religion (do a books.google.com search for the phrase and you will find it.

In short, it is highly unlikely that Goebbels said this. As is usually the case with such quotations, no one who cites it provides a source.

Randall Bytwerk, expert in Nazi propaganda (Prof. Randall Bytwerk)

https://skeptics.stackexchange.com/questions/30683/is-if-you-have-nothing-to-hide-you-have-nothing-to-fear-a-line-used-by-joseph#40126