Fish is considered a meat if going by the dictionary definition of meat: the flesh of an animal. However, there are culinary and religious definitions that place fish in a different category.
Meat is sometimes used to designate the flesh of only warm-blooded animals. This is seen in Catholicism, with the prohibition on meat during Lent. The word used for meat in this case is the Latin word "carne," which specifically means the flesh of warm-blooded animals.
The basis for eating fish during Lent comes from the writing of the theologian Saint Thomas Aquinas, who argued that fasting should only pertain to those animals that breathe air and walk on dry land. This divide, in turn, has its origins in Judaism. Without giving a reason why, Judaism distinguishes between animals of the land, whose flesh may not be consumed with dairy products under Jewish law, and fish, whose flesh is considered to be in a separate category and is not subject to the same prohibitions against being eaten with dairy products.
In culinary terms, fish and poultry are considered separate from meat, which is typically defined as the flesh of warm-blooded, land animals, such as cows, pigs, sheep and reptiles.