Why does the black-footed ferret belong in the order carnivora?

Answer 1

Do you mean why are they classified as Carnivora or quite literally why are they Carnivora?

If you meant the former, because they are carnivores - that is, they eat meat.

If the latter, because if they were not they wouldn't be ferrets - at some point in the past, the common ancestor of all modern Mustelidae (the weasel family, of which ferrets are a part) began taking advantage of a particular environmental niche, feeding on the flesh of other animals. Over time, certain adaptations and mutations that offered an advantage gave the animals that displayed them the upper hand over competitors of the same species, allowing those animals to produce more and healthier offspring. This led to the evolution of the black footed ferret. Or, if you prefer, God made them that way.