Interesting.

Now I'm off to find how a mfing snake ever became a symbol of health.

The Rod of Asclepius takes its name from the Greek god Asclepius, a deity associated with healing and medicinal arts in ancient Greek religion and mythology. Asclepius' attributes, the snake and the staff, sometimes depicted separately in antiquity, are combined in this symbol.[2][full citation needed]

In honour of Asclepius, a particular type of non-venomous rat snake was often used in healing rituals, and these snakes – the Aesculapian snakes – crawled around freely on the floor in dormitories where the sick and injured slept. These snakes were introduced at the founding of each new temple of Asclepius throughout the classical world.

The significance of the serpent has been interpreted in many ways; sometimes the shedding of skin and renewal is emphasized as symbolizing rejuvenation,[8][a] while other assessments center on the serpent as a symbol that unites and expresses the dual nature of the work of the Apothecary Physician, who deals with life and death, sickness and health.[10] The ambiguity of the serpent as a symbol, and the contradictions it is thought to represent, reflect the ambiguity of the use of drugs,[8] which can help or harm, as reflected in the meaning of the term pharmakon, which meant "drug", "medicine", and "poison" in ancient Greek.[11] However the word may become less ambiguous when "medicine" is understood as something that heals the one taking it because it poisons that which afflicts it, meaning medicine is designed to kill or drive away something and any healing happens as a result of that thing being gone, not as a direct effect of medicine. Products deriving from the bodies of snakes were known to have medicinal properties in ancient times, and in ancient Greece, at least some were aware that snake venom that might be fatal if it entered the bloodstream could often be imbibed. Snake venom appears to have been prescribed in some cases as a form of therapy.[12]

The way the story goes... They didn't explicitly fuck up, some dude just though two snakes looked cooler than one and we've just been running with it for a few decades now. There is a story about how it was originally adopted by military personnel who transported medical supplies (along with messages so... it would kinda made sense) but the justification there does feel super cherry picked. Mostly, the accepted reasoning is that the caduceus is just a better design.

Some of us know the correct one.

And to note, when I have actually looked at medical buildings, they have the correct one.