The traditional taxonomic classification is based on the most obvious similarities between species. It has been put in place long before the idea of evolution has emerged.
Thus, using the most visible characters, the traditional classification does not accurately estimate the degree of relatedness between species, and it was not its original purpose. However, it is useful for species recognition with identification keys, or for the management of biological collections. It is easily usable by the general public. Under this classification, a fish will always be close to another fish of another species not fish.
This is actually not always true. Indeed, fish are characterized by scales and fins. Yet humans share with some fish species, such as coelacanths, another character: the fleshy and not radiated member. This last character is not present in the trout, for example. Is a coelacanth closer to a human than a trout? What should be used to establish the closest relatives: the fleshy member or the presence of fins?
In the 1950s, phylogenetic classification was created. It is a system of classification of living things whose purpose is to report the degree of relatedness between species. This makes it possible to understand their evolutionary history (or phylogeny). It does not recognize certain groups such as reptiles or fish unlike the conventional classification.
Phylogenetic classification has replaced the traditional classification in most of the scientific community and in secondary education in France.