One of my distant relatives does not believe that man went to the moon.
At a wedding, I happened to enter into a debate about this very topic with them. They insisted that all the evidence that I presented was fabricated. After spending hours (it was a wedding, I had nothing better to do), I learned the one critical question to ask in such scenarios.
"What will it take for you to change your view?".
This question forces the individual to come up with what they need to accept a viewpoint different from theirs. This can help you to know whether you even want to continue the discussion. For example, if they say that nothing can convince them, you are free to move on. Or if they come up with some items, you can try and see if you can actually get evidence of that kind.
Regardless of what they say, it drastically shortens debates like this and can help you save your energy/breath.
And yes, you should ask this question to yourself too. What do you need to accept that you are wrong? After all, that is the sign of an individual capable of critical thinking, accepting that you can be wrong too.