Pokemon learn moves in order to battle against other Pokemon. There are some Pokemon, however, that learn moves that make no sense. On the other hand, there are Pokemon who can't learn moves that make perfect sense.
It is strange when a Flying-type can't learn a certain Flying-type move or when a Fighting-type can't learn the various punches found within the Pokemon universe.
Top 5 Pokemon who don't learn moves they should
#5 - Gyarados
Prior to Generation IV, Gyarados could not learn any Flying-type moves despite being a Water/Flying Pokemon. It couldn't actually learn a Flying-type move (Hurricane) until Generation VII by leveling up or by TM.
A move tutor could teach it Bounce from Gen IV onward. It is just strange that a Pokemon, who should probably be a Dragon-type, didn't learn any Flying-type moves for a long time.
#4 - Watchog
This one is a little picky based off of Pokedex data. Watchog has a Pokedex entry that states it stores seeds in its cheeks and then spits them at opponents. It can learn Bullet Seed via Breeding, but not until Generation VII. That leaves two entire Generation appearances where this Pokemon can't learn a move that, according to its Pokedex description, it should know.
#3 - Growlithe
Growlithe can't learn the move Growl. That is absolutely ridiculous. It is in its name.
Spearow, Pikachu, Clefairy, and so many more less intimidating Pokemon can learn Growl. An actual Fire-type Pokemon based off of a dog cannot learn Growl. What?
#2 - Yanmega
Yanmega has a Pokedex entry that reads, "This six-legged Pokémon is easily capable of transporting an adult in flight. The wings on its tail help it stay balanced."
It can learn a handful of Flying-type moves, such as Wing Attack and Aerial Ace. Yanmega cannot learn the HM Fly though. For a Pokemon that can "carry an adult quite easily," missing Fly is quite a large omission.
#1 - Pidgeot, Staraptor, and Unfezant
These three Flying-type Pokemon and all of their pre-evolutions can't learn Peck. All three of these are birds with beaks. There are indications that they can use Peck throughout their Pokedex entries and even in the anime.
In the games, though, none of them can learn Peck. That is as silly as it gets in terms of Pokemon not learning moves they should.