The sort of banana republic that can generate a court order for you to do that is the same kind that would simply put a gun to your head instead. In the US, no court would order that type of equitable relief.
But, pretending that's not the case:
> As a business owner, why would you reveal it ?
Because you have principles? Backed up with at least a little bit of spine?
> You'll go to jail (or struggle in court at least) for few years, have a horrible reputation and end up poor because your company is going to lose all its user base ?
It's not clear that you would go to jail. You can simply shutdown[1]. For those that actually care about privacy, your reputation would only increase.
Not a single doubt that the authorities (everywhere in the world!) have plenty of ways to coerce businesses and their owners to collaborate if the cause is important enough.
But, pretending that's not the case:
> As a business owner, why would you reveal it ?
Because you have principles? Backed up with at least a little bit of spine?
> You'll go to jail (or struggle in court at least) for few years, have a horrible reputation and end up poor because your company is going to lose all its user base ?
It's not clear that you would go to jail. You can simply shutdown[1]. For those that actually care about privacy, your reputation would only increase.
[1] https://www.theguardian.com/technology/2013/aug/08/lavabit-e...