I'm not claiming anything about the origin of balrogs - except that being the "certain 'downer" mentioned on this thread I think I must say I have thought them to be Aulë's Maiar with no canon evidence - but surely I'm either missing something or then some people on this thread have flaws in their logic.
Arien was a fire spirit, yes. Balrogs were fire spirits, yes. But does it prove they both were originally servants of the same Vala? No, I don't think so - why should it prove that? The fact that they share the element doesn't mean, in my opinion, that they are associated with the same Vala. The Valar are not totally different or opposites of one other. If they are, in some cases, quite similar to one another (just think of Yavanna and Vána and flowers, for example), why couldn't their servants be similar to one other too?