This question already has an answer here:
(I have read this discussion but I feel it does not answer completely)
Why haven't Germans massively use chemical warfare during WW2?
The Wikipedia has a text, but for me the reasons are weak:
Stanley P. Lovell, Deputy Director for Research and Development of the Office of Strategic Services, reports in his book Of Spies and Stratagems that the Allies knew the Germans had quantities of Gas Blau available for use in the defense of the Atlantic Wall. The use of nerve gas on the Normandy beachhead would have seriously impeded the Allies and possibly caused the invasion to fail altogether. He submitted the question "Why was nerve gas not used in Normandy?" to be asked of Hermann Göring during his interrogation. Göring answered that the reason gas was not used had to do with horses. The Wehrmacht was dependent upon horse-drawn transport to move supplies to their combat units, and had never been able to devise a gas mask horses could tolerate; the versions they developed would not pass enough pure air to allow the horses to pull a cart. Thus, gas was of no use to the German Army under most conditions
This is a weak reason, as there were methods to use gas with horses during WW1 - some pictures here.
Of course one reason could be that during the Blitzkrieg the use of gas was just waste of time, but in a defensive war, when Germans used anything they could (eg. in 1945, were there are famous pictures of children equipped with Panzerfaust) this could stop enemies' advance.
I also don't believe in any ethical reasons like inhuman warfare or that Hitler forbid because his own experience during WW1. It was used in Auschwitz and other camps.
I've googled this question and there are lot of discussions on the web. But these are mainly discussions and private opinions.
I'd like to read an answer backed with sources.