Because it follows the Catholic tradition of giving penance on Fridays for the suffering and sacrifices of Jesus (who was crucified on a Friday).
You can eat fish though because only red meats count.
Fun fish fact (to me anyway): In Elizabethan times, people were only allowed to eat fish on Wednesdays, Fridays and Saturdays - partly for religious reasons but also because the Navy doubled up as our fishing fleet and we needed to keep them in the water.