Butter is in fact a diary product because it is derived from a cow’s udder. Essentially butter comes from milk which is indisputably a dairy product in and of itself. Dairy products are usually high in fat, though there are some which are reduced fat or completely non fat such as skim milk.
There are also many different types of butter and imitation butter to help accommodate some of the people who are on a diet. Nonetheless it is still categorized as a dairy product along with other things such as milk, yogurt, and cheese.