[eystein]

I see nothing wrong with the defined direction of current flow. In fact it couldn't have been different.

Current is a transport of electrical charge. In the case of electrons in a wire, the charge being transported is negative. The direction in which they move must therfore be the opposite ( negative direction) of the direction of positive current flow. Two negatives multiplied ( negative charge times negative direction) gives a positive direction of current flow.

If we imagine that the electron had been a positively charged particle, it would have been moving in the same direction as the direction of positive current flow.

On the following I am a litte on thin ice, but I believe that where you have positively charged elements as for example positively charged ions in an electrolyte, they do actually move in the same direction as the positive direction of current flow.