I'm curious about the fact that neither of the above writeups offers any evidence, nor even any rationale, to back up what they're claiming.
The bottom line here is that thief pluralizes to thieves, hoof to hooves, beef to beeves (I kid you not, look it up), wharf to wharves, and so on down the line: The rule is that a terminal 'f' turns into a 'v' when an 's' suffix is added. This is an old rule. It predates Tolkien by quite a few centuries. Anybody want to guess what Tolkien did for a living? Anybody, anybody? He was an Oxford don, and his specialty was what used to be called philology. He worked on the OED. Obviously, he didn't know as much about the English language as Ekman, but at least he wasn't a complete amateur.
Speaking of the OED: The English language is complicated. Both spellings are old. The OED gives the first usage of "dwarfs" as 1770, and the first usage of dwarves (spelled somewhat differently) as 1818. I think both you kids should get on the phone and tell them they got it wrong, because Tolkien wasn't born nor even thought of in 1818.
The word "dwarf", in general, is absolute chaos before the late eighteenth century. They've got a dozen different spellings and a long fat paragraph on derivation. It's a labyrinth.
As for "elves", the OED first sees it in 1513; "elfs" appears in 1579.
"Elves" and "dwarves" are preferable because they are more pleasing to the eye and ear as well as more consistent, as outlined above with "thieves" and so on. Use those forms. Don't make me come over there.