I find arguing with unreasonable people ups your game, so to speak. Like teaching a subject you think you know well to a neophyte or child. Not only do you reinforce your understanding and perhaps gain new knowledge along the way, but you become more competent at the art of expression and presentation. It's an exercise in mental flexibility.
It's not the arguments with such people that are the real annoyance, it's when those people consider any argument against their perspective a personal affront and act hostile towards you for an unspecified period of time.
... and finding out they're in the right is possibly the most horrific event imaginable.