What is the risk of exposing our health data? To me it is not so obvious, other than maybe embarrassment? Is it like how in our culture we don't like to talk about how much money we make? Why are all these things supposed to be secret in the first place?
Imagine you used to have cancer and beat it, and independent of that fact are looking for a new job that offers health insurance.
If your condition every resurfaces, you're going to be a real expensive hire for your employer in terms of time off (for treatments and recovery) and your new health insurance provider.
You might be so expensive that they decide not to hire you, or decide not to cover you.
If you want to think of your own cases, think about medical conditions that have been stigmatized over the course of history and how people's actual lives are effected by them.