Bill, you asked: "What would YOU prefer we do to find and attempt to eliminate terrorists in this mountains? Should we just pack up & leave?"

Bill, it is the American and other invading foreign coalition troops who are the primary terrorists involved in the Iraq and Afghanistan wars.

*(Though they are clearly not aware of that...soldiers from anywhere virtually always imagine they are among those termed the "good guys" in any conflict they happen to find themselves in...and it isn't their fault...it's the fault of the dishonest politicians and greedy power brokers who SENT them there.)

And, yes, you should just pack up and leave, because your armed forces are unlawfully invading countries which did not attack you in the first place.

Obama's behaviour in the joking instance mentioned by BB is typical of the arrogant behaviour of the commanders of great imperial powers throughout history, and, yes, it is offensive. No surprise there.