I may be wrong, but I believe it is because missionaries try to avoid even the "appearance" of evil. Because they tend to stick out like a sore thumb, and everyone stares at them, those watching might mistake an innocent hug to mean something more than just that. It might also have something to do with self control, which the Elders need a great deal of.
Of course these days, all hugging or other intimate contact should probably be avoided except in rare circumstances. If I saw two young men in suits hugging I would probably incorrectly stereotype the participants (a bad habit). While I was a missionary my mission president discontinued the hugging tradition the previous president held (har har, so punny). The exception was in the mission home around farewell time. It was never done in public.
Finally, it really is up to individual missionary preference. My fellow Elders and I hugged two sisters before leaving the MTC because we had developed an emotional relationship with them. Even though it was completely innocent, we were careful to say our good-byes a non-public area.
It could also be a convenient excuse to not hug someone you find really annoying. ;-)
