The reason for the classification scheme is to group things by similarities.
Animals, plants, etc make up the major kingdoms because they do not share many similarities. The kingdoms are broken down further into, as you stated, phylum, class, order, family, genus, species, sub-species. This is done because as you go down through, similarities diverge. For example, mammals share many characteristics, yet they are hardly all the same. A whale is hardly like a mouse, yet they share common ancestry (the mammalian ancestor).
A fox (as per my example) is a different species than a dog, they cannot inter breed, yet they share many similarities, do they not? That is because they share a commmon ancestor. Like apes and man. The limb split and the branches became different species.