... every schematic drawn by every semiconductor engineer got the arrow backwards.
As I heard it, The arrow is "backward" because Benjamin Franklin, when doing his work unifying "vitreous" and "resinous" electricity as surplus and deficit of a single charge carrier (and identifying the "electrical pressure" later named "voltage"), took a guess at which corresponded to a surplus of a movable charge carrier. He had a 50% chance to assign "positive" to the TYPICAL moving charge carrier in the situations being experimented with (charge transfer by friction between different substances, currents in metallic conductors, and high voltage discharges in air and water-in-air aerosols) and happened to guess "wrong".
Thus we say electrons have a negative charge, "classical current" corresponds to the sum of the flow of moving positive charge minus the flow of negative charge (i.e. the negative of the electron current, which is all there is in normal-matter metallic conductors), the arrowhead on diodes (and junction transistors) points in the direction of classical current across a junction, and so on.
But though it's the charge carrier in metallic conduction and (hard) vacuum tubes, the electron ISN'T the only charge carrier. Even in the above list of phenomena, positive ion flow is a substantial part of electrical discharge currents in air - static sparks and lightning. Positive moving charge carriers are substantial contributors to current as you get to other plasma phenomena and technologies - gas-filled "vacuum" tubes (such as thyratons), gas an LIQUID filled "vacuum" tubes (ignatrons), gas discharge lighting, arc lighting, arc welding, prototype nuclear fusion reactors,
Move on to electrochemistry and ALL the charge carriers are ions - atoms or molecular groups with an unequal electron and proton count, and thus a net charge - which may be either positive or negative (and you're usually working wit a mix of both).
And then there's semiconductors, where you have both electrons and "holes" participating in metallic conduction. Yes, you can argue that hole propagation is actually electron movement. But holes act like a coherent physical entity in SO many ways that it's easier to treat them as charge carriers in their own right, with their own properties, than to drill down to the electron hops that underlie them. For starters, they're the only entity in "hole current" that maintains a long-term association with the movement of a bit of charge - any given electron is only involved in a single hop, while the hole exists from its creation (by an electron being ejected from a place in the semiconductor that an electron should be, by doping or excitation, leaving a hole) to their destruction (by a free electron falling into them and releasing the energy of electron-hole-pair separation). They move around - like a charge carrier with a very short (like usually just to the next atom of the solid material) mean free path.
For me the big tell is that they participate in the Hall Effect just as if they were a positive charge carrier being deflected by a magnetic field. The hall voltage tells you the difference between the fraction of the current carried by electrons excited into a conduction band and that carried by holes - whether you think of them as actual moving positive charge carriers or a coordinated hopping phenomenon among electrons that are still in a lower energy state. Further, much of interesting semiconductor behavior is mediated by whether electrons or holes are the "majority carrier" in a given region - exactly what the hall effect tells you about it.
So, as with many engineering phenomena, the sign for charge and current is arbitrary, and there are both real and virtual current carriers with positive charge. Saying "they got it wrong" when classical current is the reverse of electron current is just metallic/thermionic conduction chauvinism. B