I agree that if you're just following a specific diet by choice, it's best to just order what you want - the server doesn't want to stand there while you explain your choices. However in the case of any life-threatening food allergies, it is probably safer to say the reason. For example, if they just think you prefer no nuts in your salad, they may simply pick the nuts off the top of pre-plated food, possibly leaving behind small pieces. If you start with "I have a life-threatening nut allergy. . ." although that can feel a little awkward, like you are making a scene, it is probably a lot safer.