A patient resists every attempt to move his arm, and when asked to open his eyes he instead screws them shut more tightly, and when asked to shake hands he pulls his hand away — always doing the precise opposite of what is requested, apparently for no discernible reason. What is this?

This is negativism, specifically its active or command form: an apparently motiveless resistance to all interference, with the patient doing the precise opposite of what is asked in a reflex-like fashion, without any discernible goal or understandable reason behind it. It is not Gegenhalten, a milder, force-matching resistance to passive movement specifically, of which negativism can be regarded as a more marked accentuation — Gegenhalten does not involve actively performing the opposite of a requested action. It is not automatic obedience, which is indiscriminate compliance, the opposite pattern to this resistance. And it is not motivated refusal, since negativism is specifically distinguished from ordinary hostility or motivated refusal by the absence of any understandable goal or motive behind the resistance.