Don't argue about belief, argue about arguments
The essence of a belief is that we own it, regardless of what's happening around us. If you can be easily swayed by data, then it's not much of a belief.
On the other hand, the key to making a rational argument is that your assertions must be falsifiable.
"I believe A because of B and C." If someone can show you that "C" isn't actually true, then it's not okay to persist in arguing "A".
The statement, "All swans are white" is falsifiable, because if I can find even one black swan, we're done.
On the other hand, "The martians are about to take over our city with 2,000 flying saucers," is not, because there's nothing I can do or demonstrate that would satisfy the person who might respond, "well, they're just very well hidden, and they're waiting us out."
If belief in "A" is important to someone's story, people usually pile up a large number of arguments that are either not testable, or matters of opinion and taste. There's nothing wrong with believing "A", but it's counterproductive to engage with someone in a discussion about whether you're right or not. It's a belief, or an opinion, both of which are fine things to have, but it's not a logical conclusion or a coherent argument, because those require asserting something we can actually test.
The key question is, "is there something I can prove or demonstrate that would make you stop believing in 'A'?" If the honest answer is 'no', then we're not having an argument, are we?
Before we waste a lot of time arguing about something that appears to be a rational, logical conclusion, let's be sure we are both having the same sort of discussion.