I've always found the term "private business" a little unusual. In the case that you're doing something you don't want to tell others, saying it's your "private business" makes sense. It affects only you and it's none of their concern. But to say that a businesses that has employees, or serves the public is private in any meaningful sense of the word is nonsensical.

Your rational is that because it's a "private business" the owner, employees and customers should be allowed to subject other employees, and customers to a proven carcinogen. On that basis why shouldn't you be allowed to deliberately expose your employees and customers to radon or asbestos? It's your business, if they don't like it they can work and consume elseware.