The tricky piece of this is that people can be right about the facts and still be wrong, or at least in complete disagreement with each other. This is because there is a latent opinion in each fact, which is that the fact matters and is relevant for the conversation at hand.
If you start from your own set of priors and are getting nowhere, you probably want to consider there might be a more relevant fact (for that person, opinion alert!) that you don't know about and aren't considering.
One time I was in an argument about whether something could be done within a six month timeframe, and when a manager dropped in and asked a few clarifying questions it became clear that the other guy was working from the underlying opinion that nobody cared at all about the deadline and they were really just arguing about whether they wanted to do it. The timeline was clearly literally impossible, but he did want to do it.
Ended up that he told manager we could do it, manager was nuts and so signed us up, I left the team, they missed it by about two years. But he had fun, apparently.
If you start from your own set of priors and are getting nowhere, you probably want to consider there might be a more relevant fact (for that person, opinion alert!) that you don't know about and aren't considering.