Aristotle was the first to systematically lay out various living things in the world. According to him, they could be divided into three categories: plants, animals and rational beings (humans). Insofar as biology is concerned, human beings are animals. Therefore, there were two biological categories: plants and animals. Carl Linnaeus extended this knowledge to cover many new kinds of plants and animals, and created more divisions below that of plants and animals. Many of our modern biological categories come from him. The highest division was the kingdom and there were two kingdoms: plants and animals. In 1866, Ernst Haeckel suggested that simple single celled organisms form a third kingdom that he originally called Monera. (He later called this kingdom Protista.) His reasoning behind this change was that biological divisions show historical ancestry (common descent). Modern taxonomists have followed this new pattern and begun a program of categorizing biological things according to ancestry. This is wrong because it is contrary to the purpose of biological categorization.
There are thousands and thousands of different kinds of biological things. There are also many possible ways to categorize them. We might categorize living things by considering how we use them. So weeds refer to plants that we do not want, trees refer to large plants that provide shade, vegetables are edible plants with a similar kind of taste and fruits are plants that have sweet parts. This kind of categorization does not help us understand the living thing. It simply helps us categorize the living thing according to our purposes for it. In fact, any external categorization will not help us understand the living thing. I might name plants according to where they are found, whether I like them, where I bought them or what they can be used for. But these things may vary even if the plant (or animal) stays the same. Furthermore, even if these things do not vary, the explanation for why they do not vary includes knowledge not related to the living thing in question. For example, the reason why pineapples are edible partially has to do with the human digestive system. Finally, even the knowledge about the living thing itself does not unify our knowledge of that living thing. So no externally based categorization scheme is proper if our goal is understanding the living thing itself.
Categorizing living things by their ancestry is an external categorization scheme. The explanation why two living things were placed in the same category would be an external fact (that it is the best fit for those two individuals given the rest of biology). Although historical knowledge is invariant across researchers, it includes both facts about the living thing itself and facts about the rest of the living things that happen to live in the world. Secondly, knowing that dogs and wolves share a common ancestry does not unify our knowledge of dog or wolf biology. Knowing that both dogs and wolves are mammals (and that being mammalian is more fundamental than being a dog or a wolf), does unify our knowledge of either a dog or a wolf.
When we categorize living things we must begin with what is most fundamental, and work our way to what is least fundamental. What is most fundamental to a living thing is the reason why it is alive. Without that, it would not be a living thing at all. Everything else that a living thing does supports the life of that living thing first of all. Least fundamental are the parts of the living thing that can change without harm to that living thing such as the length of hair, the color of hair or the growth of new branches. Nowhere in this scheme is there room for facts about the ancestry of living things.
The purpose of categorizing living things in biology is to organize them in order to understand them in themselves. The purpose requires categorizing living things according to differences in those living things beginning with the most fundamental differences. Since the differences between living things are purely internal, there is no room for history. Therefore, classification schemes such as cladistics that are based on historical relationships between organisms are universally wrong.