It is a bit confusing, but there are several traits that may give Snubbull it's species.
Firstly, it's appearance says a lot of untrue things about this Pokemon. Take a look at these Pokedex entries.
>By baring its fangs and making a scary face, Snubbull sends smaller Pokémon scurrying away in terror. However, this Pokémon seems a little sad at making its foes flee. - Pokemon Ruby and Sapphire
It has an active, playful nature. Many women like to frolic with it because of its affectionate ways. - Pokemon FireRed
Fairies are popular among women, just like Snubbull is. Snubbull is a pink Pokemon and also seems to wear a 'dress', which may make it more fairy-like in a way. Snubbull may not look like a fairy, but how it acts may be why the Pokedex calls it the Fairy Pokemon.
Honestly, the only way we are going to get a definite answer is by asking Game Freak.