Why can't people like me with tmj chew gum?

Very Obvious...: Tmj is directly related to the forces that are applied to the articulation (TMJ) and they suffer the pressure of such forces (that may be up to more than a hundred pounds). If you have TMJ problems, you don't want to abuse this area that is already hurt. It would be like forcing a door which hinges are broken.

Chew gum: Pain in the TMJ is due to overuse of muscle and ligaments. The treatment, like any injured muscle, is rest ( wearing a night guard or staying on a soft diet, prevents overuse of muscles causing them to "rest"). If a patient has active TMJ pain, chewing anything vigorously and continuously will aggravate the problem.

Irritating a wound: Chewing gum is often like scratching a wound which will not allow it to heal. The same with tmj/tmd. Chewing gum, for some people, may aggravate the problem and will not help. Tmj is never cured, just maintained. Chewing gum can continue to create issues.

Depends: Gum chewing, especially if excessive, can aggravate a TMJ condition. In your case, if done judiciously, may not be a problem. It it aggravates your TMJ, bad - don't do it. If it has no effect, no problem - do it.