I saw the thread title, and jumped in, because I've got one of these. And then I realized it was a zombie.
Well, you know what BikeForums is like: resurrect an old thread and it's "Zombie! Start a new one!"; start a new thread and it's "We've had a thread on that! Use 'search'!"
AFAIK the design is by Burroughs. I think done to save weight. It also makes fixing flats easy. Myself, I would like fenders but that would be contrary to the design.
Yes, Burroughs, one of the greatest bicycle designers of our time - although not every thing he tries quite works out. He's been designing single sided frame+wheels since at least the Windcheetah days and has a chapter on this in his book. The Halfway was done during his collaboration with Giant, which brought the road bike world the now ubiquitous 'compact' frame. The Halfway idea was, as some have already said, to make the folded bike thinner. As Isinfallen points out, this introduces other secondary compromises. C
'est la vie.
BTW, the Strida folding bike has been single-sided front & rear since the mid-1980s and has always had fenders.