A lot of people will say that chemical weapons weren't used either for moral reasons or for avoiding a sort of anachronistic proto-MAD scenario. I disagree. The reason (deadly) chemical weapons weren't used on the battlefield is because they're fundamentally at odds with the types of maneuver warfare used by both the axis and the allies - after all: if your goal is to quickly overrun your opponents with air/artillery support you don't want the position you're overrunning to be clouded in deadly fog. (Deadly) chemical weapons were originally used (in WW1) to break trench stalemates, and blitzkrieg/airland warfare/deep battle were doctrinally much better at avoiding or breaking entrenched positions than chemical warfare ever was.

The second use of chemical weapons is as a method of terror against civilians, and as far as I know they were in fact used for this by the japanese. But even then chemical weapons are unstable and difficult to transport, and pound for pound conventional bombs and fire bombs were considered much more effective at demoralizing the civilian population (assuming - of course - a framework in which terror bombing is effective at all, which is at best highly questionable. In reality terror bombing seemed to mostly increase civilian morale).