How about you step back from my Psychic ace before I cleave you in twain with my main ace, you bootlegged, human-hatin', reclusive, armless, careless, brain-numbin', sound-hatin' twat?

I guess it is because they share the same typing (Psychic/Fairy) and have a similar evolutionary path (Blinding Bangs kid → Little Girl-like → Waifu-like), while having contrasting personalities (Gardevoir being a motherly guardian to their trainer, Hatterene beating the shit outta her trainer if they make a sound). That GIF of them fightning probably helps, assuming it wasn't outright what started this in the first place.