From the point of view of natural history, both the concepts and characteristics of the monophyletic group, phylogenetic systematics and natural classification system have been clarified. Natural classification system is a taxonomic system and natural evolution process of all members in the monophyletic group and their phylogenetic relationships. Only a monophyletic group including all extinct and extant members can be called a natural taxonomic system. At present, systematic biology mainly uses the cladistic principles and methods to reconstruct an evolutionary tree. During the preparation and application of a variety of system programming languages, researchers often focus on the morphological and molecular data acquisition, and the operating and calculating process, but largely ignore the hypotheses and associated weakness of the parsimony principle and the maximum likelihood or Bayesian inference. There are two common misunderstandings in the process of phylogenetic reconstruction: (1) a monophyletic group is claimed as a natural system due to incomplete selection of ingroup members; (2) a parsimony or likelihood phylogenetic relationship through mathematics and program operations is claimed as a natural evolutionary system. A natural monophyletic group often has a long evolutionary history and cannot be directly observed in nature or repeated in the laboratory. The systematical relationship among a monophyletic group established by cladistics principles is only the maximum parsimony or the likelihood speculation, thus, cannot truly reflect the development process of natural history. Fossils can provide better spatiotemporal framework information, but the number and accuracy of the available features are not sufficient. Living organisms have various abundant characteristic and genetic data. However, due to their long evolutionary history and the lack of a large number of important extinct members, the most deduced phylogenies are paraphyletic group or polyphyletic group and cannot constitute a natural system. It is impossible to construct a natural system of the whole monophyletic group by using only macro and microinformation of extant organisms. With the help of various techniques and research methods, the optimal approach to study a natural system is to combine the morphological and molecular data and integrate the whole ancient and modern members. In this process, six principles can be used to test whether the classification system is consistent with the development of natural history.