I've read discussions on other message boards about Natural Turn, and though it's been a long time, I remember the sword theory having been debunked (or at least, hotly challenged). One of the arguments against had something to do with the idea that men of the era would never have worn their swords, or even their sword "holster" (sorry, don't know the proper terminology) while dancing with a lady. Sounded convincing to me.
At any rate, that's an answer to an entirely different question, which is, "How did it come to be that dancing first began with couples turning to the right? Why not to the left?". The original question was of terminology: "Why is the right turn called Natural, a left turn Reverse, and not the other way around?". This has a much simpler answer.
For whatever reason, sword or no sword, dancing Waltz for many years was traditionally done in only one direction: To the right. It wasn't until later that someone decided to try it the other way. Since this was a variation of the norm, it was only natural (no pun intended) to refer to it as the "reverse". I read somewhere that it became customary at some point for a gentleman to ask of a new partner, "Do you reverse?".
So from a historical standpoint, it makes perfect sense: If people were turning only to the right for many years, then added a left-turning variation later on, it seems perfectly logical that the late-comer would be dubbed "Reverse".
I hear this question quite often, and I understand why. In America we are usually taught the "Box Step" -- a basic version of a Reverse Turn -- as our very first dancing pattern. Unfortunately in chain schools, some dancers pass through the levels without ever really learning to dance a proper Natural turn! If it is taught at all, it is often done only as a novelty, then forgotten shortly thereafter.
In its modern form, the Natural turn is somewhat more difficult for beginners, and so without proper guidance they fall back into familiar territory, the Left Box. To someone like this, it is understandable that they perceive a left turn as the more "natural" version. Even with proper guidance, just having been taught the Left Box first, coupled with the fact that it's somewhat easier to a newcomer, is enough to leave someone with the impression of the Left Box as the "natural".
To undo this impression, it helps to give a short demonstration of the historically-accurate version of 18th-century Waltz (aka "Vintage Waltz"). In tempo, it's Viennese, but the movement is almost more like a 3/4 Polka: A sort of a loose "side-close-close" action, where most of the turn is on the close-close. Try this yourself and you'll find that turning to the right is actually slightly easier than turning to the left. If my description isn't working for you, just try Polka turning to the right, then to the left... You'll discover the same thing.
Regards,
Jonathan