Most olive oils have a low smoke point, so when they reach temperatures of around 360 degrees Fahrenheit, they start to break down, burn, and add odors to your food.
When olive oil breaks down, it begins to release acrolein, so even if you cook your burgers perfectly without burning them, they can still taste a bit like a campfire.
Good olive oil is expensive, especially extra virgin varieties, and it's a waste of money to slather it all over the grill only to watch it go up in smoke.