"The burden of proof is on you."
No, most of the time the burden of proof is on both parties. In complete absence of any evidence both the statement and its logical negation have equal weight. So if one party states "you can't predict the shape of the bottle the liquid was poured out of from the glass it is in" and the other party states the opposite, the burden of proof lies on both parties to state their respective evidence. Of course in the special case above the disagreement was about the exact meaning of "can" or "can't" but the general principle still holds. For any given closed system the number of molecules will be either even or odd. So any arbitrary choice of statement will have to be justified. The burden of proof lies on either party claiming the truth of either position.
"The burden of proof is on you."
A burden of proof depends on the context. If you want to convince me to adopt then you have to fulfill a burden of proof and convince me that's a good decision for me to make. If you want simply want to talk about your experience that your new dog is awesome, you don't have to fulfill any burden of proof to me.
If a company wants to bring a new drug on the market they have to establish it's clinical benefits in two statistical significant clinical trials. On the other hand adverse effects have a lower burden or ...
You know the drill - If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
And, while this is an accidental exception, future open threads should start on Mondays until further notice.