> "The only thing you can do is to fork the conversation before it made the first mistake and give it more context or tell it to look things up."

This is a key detail that many folks don't seem to understand about LLMs in general. The generation of a response happens based on the model weights and the context window (the system prompt + everything it's fed about the conversation thus far + any additional data included as part of the overall prompt). Each response technically stands alone and is generated entirely from only that context given to it and the model's existing "token space" weights. The illusion of an ongoing conversation is maintained "behind the scenes" by keeping that "context window" updated with the current state of the conversation as context for the next prompt, but the next response is technically an entirely new generation of text.

What it all means in a TL;DR sense is that the fix for a refusal is not to continue the "argument", but simply to remove that entire interaction from the conversation entirely as if it never happened and try a different tack with new / updated / more complete context to get the response you're expecting / seeking.