[yarg]

That explanation seems wrong - or rather it seems to address a completely unrelated question.

The convention by which an electron is negative and a proton positive is arbitrary and could be flipped;

Indeed it could be replaced by any pair of charge definitions x and !x.

However that has zero impact on the direction of a current's flow through a conductor (that's a physical process and is not defined or impacted by the established conventions).

I'm not sure what the real answer is, by my high school physics teacher told me that the charge is carried not by the electrons, but by the gap (a virtual particle) that flows backward as the electrons move forward.

(Similar to the way that a gap in traffic propagates backwards.)

I have no idea how wrong this is, so hopefully check the comment below from whoever bothered to correct me.