I will disagree, you have no right to both keep secrets and allow other people to know them. I think blackmail should be illegal in the case of threatening to disclose criminal activity. But that case has nothing to do with the right to keep secrets. It should be illegal because it's essentially using the threat of state violence for personal gain. Any threats of violence for personal gain should be illegal.

I will note even with this limited scope it gets complicated. For example if you are being harassed and threaten to report the aggressor for criminal harassment if they do not leave you alone you might be commiting blackmail.