In the absence of facts, be creative...
Building on the idea that "Dry" is an antonym for "Sweet", perhaps "Dry Hopping" is...
The adding of hops after the yeast has consumed most of the sugars, when the wort/beer is comparatively no longer sweet.
I'm not claiming any proof that this is the origin of the phrase, just a completely unfounded yet apparently solid guess.
-- edit in response to down vote --
Could someone please suggest how I could have phrased the answer above to better avoid the negative responses? I admitted that my idea was just a guess, but I stand on it being a solid guess.