>Fairy Pokémon are mostly cute Pokémon, or majestic in their appearance.
As you can see, the Fairy egg group is for cute or regal Pokémon, not just Fairy-types. Pikachu is – although this is a matter of opinion – generally considered a "cute" Pokémon, and therefore deserves its spot in the Fairy egg group. Also note that the Fairy egg group was created long before the Fairy type. There are some Pokémon in that group that learn zero Fairy moves, such as Breloom and Glalie.
And anyway, what's not to love?