What if you were asked to "prove" that the world was not flat, could you do it? I would guess that you can provide strong evidence, but not proof—at least not in a logical or mathematical sense. The flat-earthers might then tell you that neither one of you can "prove" your claim, therefore, both claims are equally as valid (or both "faith" based). Nonsense! In the absence of logical or mathematical proof, we compare evidence. The claim with the greatest evidential support is the stronger claim. Of course, many people are politically, religiously, or financially motivated to seek out only evidence that supports their position (confirmation bias) and ignore or dismiss the rest, but that's fodder for another post.
If someone asks you to "prove" your claim, unless you are using deductive logic or mathematics, let the other person know that the truth of your claim rests in the strength of your evidence, and there is nothing wrong with that.