Shifting the burden of proof in a standard debate with external judges is pretty common.
If two politicians are debating and a group of one hundred spectators are the “judges,” the arguments don’t have to be valid or sound – they just have to convince the crowd.
If one politician senses that the crowd wants to believe his claim, he can say, “Prove me wrong,” and the other politician has to work much harder.
Vulture turned off comments because a commenter said “Prove me wrong.”
However, this little dance of theirs has no stopping point.
When there are just two people dancing around the issue, there are no external judges.
And thus the burden of proof shifts endlessly. Each dancer is unwilling to be convinced of anything new, and each dancer says to the other, “You have to convince me to MY satisfaction that I was wrong.”