Why is fish not classed as meat?

Technically, fish really is meat:
Animal: 1. A sentient living organism typically capable of voluntary motion and sensation: distinguised from plant.
Meat: 1. The flesh of animals used as food, esp. the flesh of mammals as opposed to fish or fowl. 2. The edible part of anything. 3. Anything eaten for nourishment, as in meat and drink.
http://medical-dictionary.thefreedictionary.com/animal

However, certain people have felt the need to distinguish between the two: The difference between fish & meat is the cold/warm blooded distinction.
https://www.healthline.com/nutrition/is-fish-meat

The Catholic religion follows a latin word that specifically excludes fish, seafood, and insects from the definition.
http://hubpages.com/hub/is-fish-meat

The Torah says "do not cook a kid in its mother's milk".
The oral tradition tells us that (in the Torah's classic way of conveying many messages through limited words) the Torah is teaching us many laws through this enigmatic verse. For example: "kid in its mother's milk" is not limited to a young animal in its biological mother's milk, rather the Torah is describing the general definition of meat for this law. One of the criteria for "meat" in this context is that its mother gives milk.
http://www.askmoses.com/en/article/146,2195154/Are-chicken-and-fish-considered-meat-and-not-allowed-with-dairy.html

Meat is animal flesh that is used as food. Most often, this means the skeletal muscle and associated fat, but it may also describe other edible organs and tissues. The term "meat" is used by the meat packing industry in a more restrictive sense—the flesh of mammalian species (pigs, cattle, etc.) raised and prepared for human consumption, to the exclusion of fish and poultry.

https://en.wikipedia.org/wiki/Fish_%28food%29