1.
futile argument; endless dispute; fruitless debate
An argument where both sides keep repeating their positions without any possibility of resolution, like two farmers splashing water at each other over irrigation rights.
水掛け論になった。
It turned into a futile argument.
Etymology
Originates from disputes between farmers over water rights for their rice paddies. When two farmers each claim the other is taking too much water, they splash water back and forth — an action that resolves nothing.
Usage
Often used in the pattern 水掛け論になる (to become a futile argument). Implies that neither side can prove their case and the debate is pointless.