I am basing this on what I had heard in yeshiva a while ago, so I don't know the exact source of the reasoning.
My understanding is that according to the Torah, birds (poultry) were considered parve and could be eaten with dairy. However, the rabbis placed a restriction (gezera) on birds making them fleishig (meat) as they were worried that people would get confused and think that other animals would be parve as well.
I'm uncertain as to why there would be any confusion. Birds have wings, so they are easily recognized as being different in appearance than sheep or cows. What was the concern?
If the concern was regarding all living creatures / animals, then, why wasn't the concern extended to fish and place the same gezera on fish making that fleishig as well so that people wouldn't be confused?