> Do you have a right to force the other person to keep your conversation private?

It depends. If you're speaking to a doctor or a lawyer, yes, by law they are bound to keep your conversation strictly confidential except in some very narrow circumstances.

But it goes beyond those two examples. If I have an NDA with the person I am speaking with on the other end of the line, yes I have the "right" to "force" the other person to keep our conversation private given that we have a contractual agreement to do so.

As far as OpenAI goes, I'm of the opinion that OpenAI - as well as most other businesses - have the right to set the terms by which they sell or offer services to the public. That means if they wanted a policy of "all chats are public" that would be within their right to impose as far as I'm concerned. It's their creation. Their business. I don't believe people are entitled to dictate terms to them, legal restrictions notwithstanding.

But in so far as they promise that chats are private, that becomes a contract at the time of transaction. If you give them money (consideration) with the impression that your chats with their LLM are private because they communicated that, then they are now contractually bound to honour the terms of that transaction. The terms that they subjected themselves to when either advertising their services or in the form of a EULA and/or TOS presented at the time of transaction.