Exactly why should you not mix ammonia
In a nutshell, the combination produces corrosive substances in your airways that cause your lungs to fill with fluid. You drown.
Household bleach is usually about 5% sodium hypochlorite (NaOCl).When mixed with ammonia (NH3), mono- and di-chloramines are formed: NH2Cl and NH2Cl2. These cause respiratory tract irritation, tearing, and nausea.
Worse, these compounds decompose in water to form ammonia gas (nasty in itself) and hypochlorous acid. This last in the presence of water forms hydrochloric acid and nascent (monoatomic) oxygen, which are highly reactive and can lead to pulmonary edema and pneumonia.
Don't mix bleach with phospate-based cleaners, either: that releases chlorine gas (quite nasty), which in water also produces hydrochloric and hypochlorous acids.
Since I'm a tree-hugger I'll add that citrus-based solvents or good old cider vinegar do an excellent cleaning job without the side effects above, plus they cost less and don't fsck with the downstream water supply.