Do not go in head-first, do not argue the main point. Your professor is comitted to his side and the more you argue logically, the more he'll dig his heels in.
Look for small commitments. Don't ask him to jump into the water, just ask him to dip his toe in.
Here's an example: in the 90s, many people were vehemently anti-Apple. There was a huge Microsoft/Apple divide, and there were great religious debates going on. How do you convince someone to switch? Not by extolling the virtues of the system. Because the harder you argue, the more they'll dig in. The way to convince them is to buy them an iPod shuffle for their birthday. That's a small commitment. A tiny little step that forces them out of their black and white worldview. They can keep their Windows laptop, and its ecosystem, but one tiny device in their life now comes from Apple. And suddenly the idea of owning Apple products doesn't seem so inconceivable anymore.
This is easiest to achieve if you don't have the religious debate beforehand, so they won't be suspicious of you. You have the luxury of planning your strategy before your professor knows your position. So avoid the religious debates at all cost, and take the position of not having a position. Then look for the tiniest little commitment you can get him to make: maybe that the research is not conclusive yet, that in certain cases, his method is not optimal, that it would be good to have a constructive discussion with the other side, etc.
I actually had this with my supervisor, and we managed to change his view towards the end of the project . Here are some more tips that will make your life easier:
- Maintain an agnostic position. Without undermining him, discuss your view of the research at all times. Let him make his ambitious promises, but don't go along if you don't agree.
- Be up front about your agnostic position. You are going into the research with an open mind, and you may not end up seeing eye to eye.
- Find an ally. If it's you versus him, the power differential will make it difficult to maintain your position. If there's a postdoc arounds who can also put a dissenting position forward, the whole thing becomes a open discussion.
Basically, you're in a difficult position. You also have a PhD to finish, and that's a difficult task even in supportive surroundings. However, you're going in with the right attitude. Your aim should be to take no sides, and to investigate the question fairly, and to ultimately resolve the debate. If you manage that, you will have made a solid contribution to the research, and your career will be off to a good start.