Following is from wikpedia:
Under the traditional nomenclature codes, such as the International Code of Zoological Nomenclature and the International Code of Nomenclature for algae, fungi, and plants, taxa that are not explicitly associated with a rank cannot be formally named, because the application of a name to a taxon is based on both a type and a rank. The requirement for a rank is a major difference between traditional and phylogenetic nomenclature. It has several consequences: it limits the number of nested levels at which names can be applied; it causes the endings of names to change if a group has its rank changed, even if it has precisely the same members (i.e. the same circumscription); and it is logically inconsistent with all taxa being monophyletic.
Especially in recent decades (due to advances in phylogenetics), taxonomists have named many "nested" taxa (i.e. taxa which are contained inside other taxa). No system of nomenclature attempts to name every clade; this would be particularly difficult in traditional nomenclature since every named taxon must be given a lower rank than any named taxon in which it is nested, so the number of names that can be assigned in a nested set of taxa can be no greater than the number of generally recognized ranks. Gauthier et al. (1988) suggested that, if Reptilia is assigned its traditional rank of class, then a phylogenetic classification has to assign the rank of genus to Aves. In such a classification, all ~12,000 known species of extant and extinct birds would then have to be incorporated into this genus.
What is the precise meaning of "it is logically inconsistent with all taxa being monophyletic"?