I'm totally with your DS on this. I find gum unbearably gross, and anything that makes me aware of it is a problem, whether it's the noise, the sight, or whatever.
The source of this aversion is heterogeneous. It's having seen (and creepily, accidentally touched) old gum stuck under school desks and movie seats. It's the chewed shape that gum takes on, when it's spit out or when it's visible in someone's mouth. It's the sound. It's the absent-minded way that people use it as a way to fidget, but with their mouths. It's the fact that it keeps being in their mouth, all spit-covered and being rolled around. It's the fact that the way it's going to leave the person's mouth eventually is by being spit out. It's the way a person will tuck their gum between their teeth on one side while they're talking to you, so you see it bobbing in and out of view.
So anything that makes me aware that someone is chewing gum triggers this whole sensory complex of awareness-of-gum-chewing. Maybe your DS has something similar going on?