If you and I have a disagreement on whether something exists or not, we can resolve it in the following way:
Assume we each have the same amount of knowledge about the world, i.e. we have the same background information.
Assume that you feel that "X" exists.
Assume that I have never experienced anything that leads me to believe that "X" exists.
We can conclude that only you have a motive to present a case for the truth of your belief that "X" exists, because I, not having this belief, have no motive to develop a case about “X”, one way or another.
The responsibility resides with you to make your case about “X”.
It’s that simple.