Why you should never exercise American options?
Actually a better question is, why you shouldn’t early exercise your american call option? Early exercising American call option on a non dividend paying stock is not optimal for two reasons. One delaying exercise delays the payement of the strike price. This means that the option holder is able to earn interest on the strike price for a longer period of time.
Second assume that you exercised your option today, what if tomorrow a big crazy thing will occur and the price of an underlying asset just shoots? Sorry baby you already exercised your option and you sold your right to buy at a very cheap price. Instead of exercising your American call option you should have sold it to someone else.