It's funny to think that all electrical components, including diodes are engineered in a way where wiring them up the "wrong way" according to human intuition but correctly according to the schematics, makes the whole thing work. Then we decided to throw negative DC voltages or AC into the mix to make things even more confusing, which essentially just shift the reference point for what we would usually consider as "ground" in a circuit. All of this just to make the math work out in the end, and I think that's pretty neat.

We call this "technical" and "physical" direction of flow

When you get into electrochemistry, the answer becomes complicated. Positively charged molecules move too, and in semiconductors there's such thing as a 'hole' - an absence of electron in a densely packed electron field - which carries charge as if it were a real particle.