There is no 'good' argument to persuade anyone (of anything) the moment they don't want to change their mind. But, depending who your talking to, asking a question maybe? More often than not the 'nothing to hide' is just an excuse to not change their habits (which is their right), exactly like the 'I don't have time to read books' so, so many people use today to explain why they never read.

What questions? Well, first, I would not do that. to be clear. But if I really wanted to force them to realize they have things to hide, like we all have, I would go for the most intimate/unsettling... depending who I am discussing with:

Did you poop today? And was it easy? (this one should be both easy to answer while being considered so intimate, at least to most people, that they should have a hard time answering it without feeling disturbed).
How much do you earn?
How much do you pay in taxes? (or how do you manage to not pay taxes?)
How often do you have sex? What is your favorite position? or How reacted your spouse when you told them about that little affair you had with someone else? (here again, it all depends the person you're talking to)

And so on.

I insist, it is not something I would do but I also have little doubts most people would instantly feel like they too can value some privacy and intimacy ;)