Then why are things which are fermented to "dryness" dry and not sweet?
Maybe you're thinking of 2 different definitions?
Sweet is a flavor
Dry is a mouthfeel
Perhaps I should have elaborated more. I'm basically in the same camp as Dave. I've never perceived alcohol as sweet. A specific example would be clear spirits. Something like vodka very much doesn't come off as sweet to me. That said, I definitely admit that things will taste different to different people.
On the topic of a hypothetical sugar solution fermented to dryness (let's say 0.992 which was mentioned in a reply), I wouldn't expect the resulting liquid to have a sweet taste. I could be wrong because I've never done that specifically. But I've had honey ferment as low as 0.990. This again would be a matter of taste perception, but I can't imagine anyone who would have described that mead as having a sweet flavor.
It's true that dry beer can still have a sweet flavor. But I would tend to attribute that aspect of the flavor to other parts of the beer, not the alcohol. Not sure though. I could be wrong.