I must admit that I never understood this question. The two statements are not exclusive so what kind of idiot thinks that a glass is half full while not being half empty or vice versa? How can it be half full without being half empty or vice versa? In order for it to be half full the other half needs to be empty (or vice versa), so not only are the two statements not mutually exclusive, they directly imply each other.
The question is usually asked in order to determine one's outlook. The problem with the question is that it implies there are two answers, when in fact there are four:
The pessimist: "This is terrible! I've already consumed half of my beverage!" :sadvaultboy:
The optimist: "This is great! I still have half of my beverage!" :rock:
The literal minded: "There is no difference. Six of one, half a dozen of the other." :grad:
The engineer: "The glass is the wrong size." :shrug:
The belief is that which ever viewpoint you present gives an indicator of your overall view. The problem with that belief is that a person's mood at the time of questioning can influence the answer.