Oh, how I wish this weren't a myth.
Most of our bodyies' fat is in a layer just under the skin, and on top of the muscles. Muscles and fat are two different layers. How much fat you have is determined basically by the balance between how much food energy you eat, and how much energy you burn. When you body has extra energy, it stores it as fat. When in needs more energy than it takes in, it uses fat. There are other influences (genetics, food type, etc).
How that fat is distributed on your body is determined by genetics. Some people have proportionately more on their bellies, others distribute it more evenly. Also, where you put on fat first is genetically determined. Usually the areas where it accumulates first are the last places for it to go when you lose.
Exercising a muscle requires energy. That energy is taken from substances in the blood. Those substances are the product of metabolic processes that take place throughout the body, particularly in the liver. The fat that provides the energy for a particular muscle does NOT come just from the fat that is stored near that muscle, but from the body's whole fat stores.
Therefor, exercising your left arm does not remove fat from the left arm any more than it removes it from the whole body. If you have an area with fat that you want to get rid of, you have to get rid of fat from your whole body through a combination of eating less, eating smart and exercising more.
Further, exercising a muscle does not make it smaller, it makes it bigger! So if you have a part that you want to make smaller, and you've already lost all excess fat, the best thing is to not exercise it at all, but just put it in a cast and wait patiently for the muscles to atrophy.
(Just in case there are people reading this who don't get sarcasm, I DO NOT advocate putting a body part in a cast to make it artophy.)