In order for it to be Flying, Gamefreak would have to retcon what constitutes an Eeveelution. Their aesthetics are associated with their type, as is the prefix of their name. In fact, Eeveelutions epitomize the type they forecast through appearance; this is not a loose relation, either. The theory that there may be a new type is interesting and fun but demands logical representation, and there's just too much to analyze to reasonably conclude that they would create a new type when the meta-game doesn't really warrant it. But the showcasing of the mystery behind this Pokemon (a Pokemon whose revelation would automatically send us into speculation upon its type, as its evolutionary line epitomizes the relation to its physiology and type) also begs the question as to what type it is, and why it's important for that type to be hidden (in an Eeveelution, of all Pokemon).
The question as to why it's Flying bothers some not because we want to start fires and spew vitriol in the form of E-arguments, but because if it was Flying, it would undue the natural representation Eeveelutions bare; it make little sense in its representation as opposed to another more fitting type. Why it could be a new type is a theory based on the strange anonymity to its type. And yes, some of you can fallaciously draw similarities to other (new) Pokemon having types (originally) hidden from knowledge, but this is a Pokemon, as said ad nausem, that comes from a line that always reflects to us its type in a fashion that is undeniable. Gamefreak doesn't normally play guess-who with Eeveelutions, so that's why this debate forms. It's also fun to speculate and debate, and even somewhat healthy if we avoid shaming and blaming.