Okay, so everyone has kinda assuming that their will be a new eevee evolution. Mostly thanks to pokemon smash, and the the new movie having the eevee at the end. But let's have a look at eevee and his evolutions.
1st Gen (3 evolutions and eevee himself) Eevee Flareon Vaporeon Jolteon.
Now Flareon has a weakness in type to water (Vaporeon) and Vaporeon has a weakness in type to Electric (Jolteon)
2nd Gen (2 new eeveelutions) Espeon Umbreon
And here we have Espeon, who has a weakness in type to Dark.....oh, wasn't Umbreon a Dark type.
4th Gen (2 new eeveelutions) Leafeon Glaceon
Do I need to spell this one out. Grass has a weakness to Ice.
Now it's sixth gen and there's a hint or rumor for a new eevee evolution, but under the looks of things. It always tends to be two new evolutions at once. And one normally has a type advantage over the other.
So what two eeveelutions could we expect. Flying<Rock, Rock<Fighting, fighting<flying, Ground<Flying, rock<ground, Poison<ground, Rock<Metal, bug<poison, Bug<flying (probably missing some others, but meh.)
TL:DR If we're getting a new eeveelution, they've always come in pairs, and one is normally type advantage over the other. --- Sic vis pacem, para bellum