The living forms were the basis of most of our biological taxa in the first place. Thus, living forms fit said taxa well and extinct forms tend to blur or straddle the edges.
The forms always display convergence as you go back in the fossil record, divergence as you go forward. There's no problem telling any modern reptile from any modern bird, but there are fossils whose status has been argued or switched between the bird and dinosaur groups. As you go back in time, whales and sirenians get legs, as their relationship to their non-aquatic ancestor groups becomes less distant.
From Taxonomy, Transitional Forms, and the Fossil Record, we have the following.
That is, you don't expect to have any trouble telling a mammalian carnivore (dog, bear, cat, racoon, etc.) from an ungulate (horse, deer, antelope). If you didn't believe in evolution, you might not expect to see their ancestors get more and more like each other as you go back in time, either, but they do. It's a prediction of evolution. It's the expected signature of common descent--a branching tree thereof.Moving further up the taxonomic hierarchy, the condylarths and primitive carnivores (creodonts, miacids) are very similar to each other in morphology (Fig. 9, 10), and some taxa have had their assignments to these orders changed. The Miacids in turn are very similar to the earliest representatives of the Families Canidae (dogs) and Mustelidae (weasels), both of Superfamily Arctoidea, and the Family Viverridae (civets) of the Superfamily Aeluroidea. As Romer (1966) states in Vertebrate Paleontology (p. 232), "Were we living at the beginning of the Oligocene, we should probably consider all these small carnivores as members of a single family." This statement also illustrates the point that the erection of a higher taxon is done in retrospect, after sufficient divergence has occurred to give particular traits significance.
Figure 10. Comparison of skulls of the early ungulates (condylarths) and carnivores. (A) The condylarth Phenacodus possessed large canines as well as cheek teeth partially adapted for herbivory. (B) The carnivore-like condylarth Mesonyx. The early Eocene creodonts (C) Oxyaena and (D) Sinopa were primitive carnivores apparently unrelated to any modern forms. (E) The Eocene Vulpavus is a representative of the miacids which probably was ancestral to all living carnivore groups. (From Vertebrate Paleontology by Alfred Sherwood Romer published by The University of Chicago Press, copyright © 1945, 1966 by The University of Chicago. All rights reserved. This material may be used and shared with the fair-use provisions of US copyright law, and it may be archived and redistributed in electronic form, provided that this entire notice, including copyright information, is carried and provided that the University of Chicago Press is notified and no fee is charged for access. Archiving, redistribution, or republication of this text on other terms, in any medium, requires both the consent of the authors and the University of Chicago Press.)
For any other model of the diversity of life, the evidence I've just described is a shrug and a wave-away. One must dismiss the evidence, claim that all 150 years worth is a Piltdown fraud, or just say "God could have left the fossil record looking like that. After all, He could have left it looking any way He wanted."
Everything in the present is at a branch tip on the tree of life. Some things do seem to show an intermediate character between things on other branches (those egg-laying monotreme mammals, for instance) but everything is in fact on its own branch tip and everything is the result of billions of years of evolution. That's the evolutionary model and it's the only one that makes any useful sense for understanding what we see. There's nothing else. Wave-aways and patent evasions don't cut it.