Finneon and Lumineon get Silver Wind via level up, being the only non-Bugs who do so. What?

Well, I think it’s because of their butterfly-wing fins.  Silver Wind is an attack associated not just with bugs but specifically with butterfly and moth Pokémon, all of whom have access to it aside from Vivillon, and they account for most of the Pokémon who learn it by levelling.  Lumineon is clearly meant to resemble a butterfly (for what reason I’m not sure, though Bulbapedia suggests a link to the freshwater butterflyfish).  The “wings” also net Lumineon access to Gust, for what it’s worth, and are perhaps responsible for her getting U-Turn as well.