The distinction has always been between warm-blooded and cold-blooded. Fish and reptiles being cold-blooded are not considered true flesh. The rational is that abstaining from meat is in memorial of the flesh and blood shed by our Lord. I guess it is some form of bloodism discrimination.
I heard that the original intent of forbidding meat on Fridays and during Lent was to save the fishing industry in Italy. As such, I do not follow this convention.