“That which can be asserted without evidence, can be dismissed without evidence.” - Hitchens's razor.

The burden of proof is always on the person making an assertion or proposition. When they do not provide proof of their claim, and another person calls it "full of shit", it is not valid to shift the burden of proof onto them to disprove the original claim.

And there's a great reason for this - the bullshit asymmetry principle: the amount of energy needed to refute bullshit is an order of magnitude bigger than to produce it.