Nested Hierachy and evolution- another refutation of the premise

Zachriel and others continue to spout off that descent with modification will lead to a nested hierarchy.

I have already provided enough reasons to refute that premise but here is one more:

Nested hierarchies have a direction-

For example in the nested hierarchy of living organisms we have the animal kingdom.

To be placed in the animal kingdom an organism must have all of the criteria of an animal.

For example:

All members of the Animalia are multicellular (eukaryotes), and all are heterotrophs (that is, they rely directly or indirectly on other organisms for their nourishment). Most ingest food and digest it in an internal cavity.

Animal cells lack the rigid cell walls that characterize plant cells. The bodies of most animals (all except sponges) are made up of cells organized into tissues, each tissue specialized to some degree to perform specific functions.

The next level (after kingdom) contain the phyla. Phyla have all the characteristics of the kingdom PLUS other criteria.

For example one phylum under the Kingdom Animalia, is Chordata.

Chordates have all the characteristics of the Kingdom PLUS the following:

Chordates are defined as organisms that possess a structure called a notochord, at least during some part of their development. The notochord is a rod that extends most of the length of the body when it is fully developed. Lying dorsal to the gut but ventral to the central nervous system, it stiffens the body and acts as support during locomotion. Other characteristics shared by chordates include the following (from Hickman and Roberts, 1994):

bilateral symmetry
segmented body, including segmented muscles
three germ layers and a well-developed coelom.
single, dorsal, hollow nerve cord, usually with an enlarged anterior end (brain)
tail projecting beyond (posterior to) the anus at some stage of development
pharyngeal pouches present at some stage of development
ventral heart, with dorsal and ventral blood vessels and a closed blood system
complete digestive system
bony or cartilaginous endoskeleton usually present.

The next level is the class. All classes have the criteria of the kingdom, plus all the criteria of its phylum PLUS the criteria of its class.

This is important because it shows there is a direction- one of additive characteristics.

Yet evolution does NOT have a direction. Characteristics can be lost as well as gained. And characteristics can remain stable.

All of that means we should not expect a nested hierarchy with descent with modification.