Answer:
Superconductivity is not by any means a classical phenomenon. Imagine the water in the pipes in your house suddenly all occupying the same space, and the flow of water is not the movement of small elements of water individually, but rather every drop of water acts together to flow in the same direction.
In technical terms the simpler superconductors involve the electrons paring up into "cooper pairs" which act as a single particle with bose-einstein statistics and condensate into a superfluid.