Systematics is the classification of organisms and their evolutionary relationships. Systematics is a broader category which encompasses several methods and forms of study of evolutionary history which attempt to place hierarchical, branching connections between species. It includes methods such as cladistics, phylogenetics, and taxonomy, but it is not necessarily synonymous with all, let alone any of these methods.
In brief, the incompatibility of systematics with all methods of classification occurs because systematic, human classification cannot be applied to biology in full. Each sub-method is a way of classification which is often incompatible to one another because they approach this human flaw differently. For example, one structure which is compatible with systematics is the Linnaean taxonomical system. However, if the ranks under this system are then placed on a phylogeny by their evolutionary relationships, the groups may be arranged to accommodate for this, and many species may not be grouped under a lineage with the same genera or ranking of higher order. One notable example in this case is the Aves clade, which would be classified by a cladistic lens as a subgroup of Reptilia.