One of the toughest cuts of the cow, brisket is best cooked low and slow. A grill is designed to apply high heat to whatever you're cooking, the exact opposite of what you need.
When grilling brisket, too much heat is applied too quickly and the muscle fibers will tighten up into a dense block. Instead, brisket should be cooked in a smoker or braised.
The brisket is full of connective tissue and collagen. When cooked low and slow between 160 and 205 degrees F, the collagen becomes gelatin, resulting in a tender brisket.
Some people can rig their grills to work like a smoker, with some success, but if you are considering using your grill normally, you're going to end up with a tough piece of meat.