Why does cooking with aluminum foil cause problems?
When food is wrapped in aluminum foil and heated during the cooking process (such as on the grill or in the oven), the aluminum in the foil basically breaks down and winds up in your food. In some cases, the researchers found that the amount of leached aluminum in the food reached levels well above the World Health Organization's recommended safe limits: 1mg of aluminum per kilogram of body weight.
Temperature, acidity, and cooking time also affect aluminum levels in fairly intuitive ways: cooking at a higher temperature, cooking with more acidic food, and cooking for longer all mean increases in aluminum levels. That's a huge bummer if you love a quick lemon-roasted chicken, grilled pineapple, and on and on and on.
Don't eat the aluminum foil
In other words, do you really want to risk chewing up and swallowing a bunch of excess aluminum if you don't have to? Probably not. While you really can't avoid coming into contact with aluminum as you go about your daily life, since you have to come into contact with drinking water and the Earth's crust, not cooking with aluminum foil is probably one of the easiest changes you can make to whittle down your exposure, especially if it's done on the regular. There are all sorts of glass, ceramic, cast iron, and other aluminum-free cooking dishes available -- and if doing dishes is a complete impossibility, parchment paper usually works in a pinch.