Dairy aka blood of a cow has allot of fat and is alkaline, unless manufacturered to have all the fat and alkaline salts removed, then your just craving poison.
"IF" meat grosses you out, think about sucking cows blood each time you drink a dairy product and maybe that will break that habit as well. Seek plant fats such as Olive Oil and see if that stops the cravings. At the very least, try goats milk or faked milk from soy or rice.