This isn't some kind of weird, esoteric form of argument. It's an underlying principle of empiricism that you should try to provide evidence for claims you make rather than making the accused prove something is false.

Someone accuses you of murder and says "prove you didn't do it". You didn't do it, but can't satisfactorily prove such a negative. Maybe you were outside taking a walk and no one can provide an alibi. Does that mean you should be assumed guilty?