I've learned long ago. Unless the reason or person is important, you need to take the time to consider whether you ought to put your efforts into trying to convince those who have long ago convinced themselves. Do it if it's worth it. But know it will never be easy.
They have to step outside of their own world, their own motives and sense of reasoning, first. They have to be willing to see, and they have to see it. But it's hardest when their biggest concern is not understanding, but saving face.
Logic isn't the problem. They'll never say it, but they want a parachute too. And they want you to take the time to prove to them that it has no holes. And only if they are certain the rest of the world will never catch them looking.