>>19933668This. Fighting type conveys an explicit meaning to the Pokémon. Mostly that it excels in combat and goes beyond simple smacks and bites to fight.
A lot of the other types either imply a state of being (flying, ghost, ice even) or a primary 'element' (electric, water, steel, etc). Fighting and Dark both imply a sort of knowledge or finesse having to do with either fighting well or being dubious.
Normal implies that the Pokémon is otherwise unremarkable, which seems to be why birds get paired with it (it can fly, but isn't otherwise special).