What's the difference between saying that the burden of proof is on one's opponent, and simply saying that they are likely wrong? The idiom of "burden of proof" is used in a way that suggests that it's somehow different from ordinary, straightforward evaluations of evidence and arguments, but I can't think of what that difference could be.

You often do hear people in philosophy say that the 'burden of proof' is on their opponent. And you sometimes hear people argue about who has the 'burden of proof'. I think that what this usually is about is which position is antecedently more plausible, or which position presently has the best arguments in favor of it. It's kind of like the game "King of the Hill". Whoever's on top of the hill is king, and someone else has to knock them off.

Personally, I don't find this way of thinking about philosophical arguments very helpful. It's not that I don't think there is a 'truth' to these matters, but philosophical progress tends not to happen in a linear manner. The fact that something seems plausible today may not be a very good guide to whether it is true. More generally, I tend to think that understanding an issue is in a way more important than knowing how to solve it, so telling me that you've given an argument and now someone else has the 'burden of proof' just sounds gratuitous. You gave an argument. Period.

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