I have an analogy for exactly this.
If we suppose we're in an office building and one of the doors is locked, we can make a few guesses about what's inside it. Perhaps staplers, papers, filing cabinets, etc. Now let's say a person comes along and tells you there's a tiger in that room. You've seen no evidence for his supposed roomtiger, and tell him this. At the same time, he's seen no evidence for documents or office supplies. Since the room is still locked, both claims are on level ground.
Now let's suppose somebody comes by and unlocks the door. The room is found to have a few desks and common office supplies. There is certainly no growling or scratching. Your side is supported while his is invalidated.
From here, instead of conceding defeat, the roomtigerist begins making many more baseless claims to justify his position, like that the tiger is invisible ("we can't see it, so it MUST be invisible"), only affects things if it wants to affect them ("it's not affecting things now, which is evidence that it only affects things it wants to affect"), and that its growls can only be heard at certain times ("just listen, I've personally heard it a bunch of times and it definitely WASN'T the construction work across the street"). He goes on to pretend these assumptions are completely scientific and claim anyone with a contrary opinion is in on a large-scale conspiracy to further conceal the roomtiger--the existence of which he feels is obvious.
Is it up to you to provide evidence AGAINST it before believing otherwise?
Why can't the roomtigerist admit it's a regular office?