No, I have to disagree. One of the "holy grails" of biology is to unambiguously determine the true tree of life. Cladistic analysis, especially that using DNA, is getting us there. In fact, large parts of the tree are already known. It's no more man-made than the periodic table.
For example, we know, way beyond any reasonable doubt, that chimps and people form a clade (all descendants of some species), that chimps-people-gorillas are another, and so on and so on: primates, artiodactyls, carnivora, a lot of the familiar Linnean orders, classes and genera of mammals, birds, reptiles, plants, fungi, etc etc.
It is known, with no reasonable doubt whatsoever, that mammals are a clade, and that birds are.
I have to restrict the discussion to eukaryotes, because bacteria and archaea trade genes in funny ways, and the definitions af ancestor and descendant aren't nearly as obvious, and also because I don't know much about them. But the scheme seems to work very well indeed for eukaryotes.
Assuming common descent, there is a clade defined by any two organisms. For example, I've seen mammals defined as the group of things descended from the last common ancestor of people and platypuses, or bilaterally-symmetric animals as the descendants of the last common ancestor of "Antlia the ant and Attila the Hun".
But there are a few surprises:
Reptiles, as commonly defined, aren't a naturally-defined grouping. The clade defined by crocodiles and snakes includes birds and dinosaurs, and, IIRC, reptiles as well. The clade defined by any green plant and any fungus includes all, again IIRC, multicellular life.
Insisting on using only taxonomical categorizations is "begging the question" (e.g. whales are mammals, and therefore evolved from land-mammals), since we are discussing the natural (not man-made) origin of species.
I'm not quite sure what you mean here. Whales are mammals, and "proto-mammal" was pretty obviously a land dweller.
Taxonomical categories describe species, but do not tell us whether one came from another. ( whales could have theoretically developed from fish without leaving the water leaving the water, while the other mammals happened to get their systems independent of what was going on with the whales.)
This hypothesis (about whales) is disproved by genetic analysis: cetaceans are clearly most closely related to artiodactyls (cattle, deer, hippo, giraffe, etc). In fact, there is a clade called the cetartiodactyls that covers these exactly.
The analysis doesn't say what came from what; it shows which thngs are more closely related to each other than to anything else; their common ancestor may or may not be found as a fossil, and it isn't always obvious which fossil correspnds to the common ancestor.
If this cladistic taxonomy were to prove impossible, it would be a serious blow to the biological theory of common descent, if not to evolution itself. Conceivably, there are some things that just refuse to be classified; so far these have not been found.
The greatest unknowns are the relationships at the phylum level: are flatworms more closely related to roundworms, or hair worms, or bearded worms, or what? are starfish more closely related to chordates than anything else? what are the relations between insects, spiders, trilobites and crustacean? are they a clade or not? This stuff is being researched, and answers are being found.