If you feel like the person you're arguing with is just hopelessly irrational, you're probably right.
For many years of my life I've thought when going into arguments with irrational people, "I know he has an emotional incentive to be irrational on this issue, but surely if I'm patient and refute all of his arguments in sufficent depth I can make it impossible for him to deceive himself". But I've learned something: the reservoir of objections is literally infinite. Someone can always raise another objection that sounds reasonable if you don't read the entire context or aren't trying to rationally evaluate it and just want an excuse not to believe in something that would shatter your worldview. And of course, as the length of the context grows it becomes easier to forget about the first couple objections that were refuted and begin recycling them with variations of the word salads.
No claim is ever sufficiently proven to someone who doesn't want to accept it. So we need to learn to give up on people.
There are still valid reasons to argue with irrational people, sometimes. Mostly if you do it in public, you stand to make a bad person look like a total retarded moron and thereby maybe, maybe, sway someone else who will listen to it at some point. Or just damage the reputation of somebody like that so they have less of a following to spread their violent ideas to.