Agnostic atheists often say that their position makes no affirmative claims, hence they don't have any burden of proof. But that's where you trap them. "I didn't make an affirmative claim" is itself an affirmative claim. It's a claim about something you didn't do. You might say this is petty and unfair. But "that's petty and unfair" is also an affirmative claim. "I don't believe x" is also an affirmative claim. Maybe you do believe x and you're lying. At this point, maybe you're tired of having a pedantic conversation about the burden of proof. But "I'm tired of having a pedantic conversation" is also an affirmative claim.
If all else fails, just ask them their name. "My name is Bob" is an affirmative claim, and now you're both in the same boat. The way to avoid getting trapped yourself is to phrase everything in the form of a question. Asking "why do you beat your wife?" or "how can you prove x?" isn't making an affirmative claim, so it doesn't come with a burden of proof. Just ask "how do you know?" to every statement they make, and pretty soon they'll have made a hundred-plus affirmative claims while you only have the one.
Unfortunately, I made a bunch of affirmative claims in this post, so it's too late for me. But maybe someone else can make use of this information.
