I have had conversations that should have been formalities, lasting only a few minutes and ending with both parties agreeing on the problem and the way forward. Instead, almost immediately the conversation takes a surreal turn when I find myself having to explain basic concepts and simple reasoning points.
Patiently, I explain the fault in the reasoning, I correct the factual error. Politely, I reformulate my replies to encourage them to see the mistake. Respectfully, I accept that I may not be clear enough so I explain again. Smiling, I explain it again. Confused, I explain it again.
At some point the thought will come to me that the best option is to give up. End the discussion. Walk away accepting that they will never understand the problem with their argument. But I can't do that: it's not a difficult thing to see, surely they will understand if I explain once more. If I explain again. Better. Louder. And so I do. And still they miss the point, the logical connection. And I am now too deep in the conversation to give up. Just one more explanation and they will get it. It feels like a trap that I am setting for myself, over and over again.
Eventually, mentally exhausted and baffled at how it could be so difficult to get someone to accept a simple concept, to see the other side, to consider another point of view, I give up. Defeated, sad and empty, I take my failure with me along with the unresolved issue.
I don't have a solution to get you to convince people who just won't listen, reconsider their views or accept that maybe they are wrong. But I have a solution to protect you from that feeling of wanting to glass yourself in the face that comes with discussions with such people.
Walk away. Recognise when this happens and walk away. Don't even try to engage them. Some questions aren't worth answering. Some things aren't worth explaining. Some things are so basic that here is nothing you can say that will get them to understand if they don't understand it already.
Walk away and find someone else who gets it that can work with you. There is no shame in giving up if you can't win.