"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.