[Physicist]

It is further shown that, if this strict monophyletic hierarchy is to be regarded to be the result of an evolutionary process, then it must be the case that (in general) evolution has proceeded in such a way that each more-generic taxon has split symmetrically into two more-specific taxons: By symmetrically I mean that each moregeneric taxon has ceased to exist as an independent entity after the split, instead continuing to exist only in the generic features of the two more-specific taxons into which it has become divided..

Total garbage. Evolution demands no such symmetry and no such symmetry is observed in nature. According to the theory of evolution, a split can be symmetrical or not. Some splits in nature are symmetrical and some are not. This is true both genetically and morphologically. Furthermore, it is not true that when a taxon splits into two, the "parent" taxon necessarily ceases to exist.

I haven't read the above article in its entirety yet, but from the blurb you posted it isn't clear whether the author is saying that evolutionary theory demands symmetrical splits and doesn't get them, or that evolutionary theory can't explain why all observed splits are symmetrical. Either way he's wrong, however.

[gore3000]

According to the theory of evolution, a split can be symmetrical or not. Some splits in nature are symmetrical and some are not.

Not correct. Neo-Darwinian evolution does indeed require non-symmetrical splits. Remember, it is the result of random mutations accumulating over time and eventually transforming at least some of the individuals into a new species. This is in no way symmetrical evolution.

For a full discussion of why the Neo-Darwinian process has been proven false you would need to read the full article which you obviously have not done. Much easier to spew rhetorical nonsense than bother becoming informed on the subject before you open your mouth.