Why is traditional rank based taxomomy considered by some as logically inconsistent with phylogenetic knowledge?
You can find discussions of problems with rank-based taxonomy in light of phylogenetics in Ereshefsky 1994, de Queiroz 1996 and Ereshefsky 2002. To summarize, the main problems they identify are:


It's hard to define what exactly an "order", "family" or "genus" is; in particular, taxa at the same rank aren't always comparable. For example, order Hymenoptera, which evolved 250 million years ago and consists of over 150,000 species, with order Carnivora, which evolved 42 million years ago and consists of "over 280 species".
Not enough ranks: NCBI recognizes 29 higher taxa for Homo sapiens. That would require dozens of sub-and-super ranks to render into Linnaean taxonomy.
Names based on ranks: current nomenclature allows certain ranks to be identified by their ending, for example names ending in "-ini" refer to tribes (e.g. Hominini, Canini). If one of these tribes turns out to be non-monophyletic, it may have to be moved to a higher or lower rank to keep its monophyly -- which would have to be renamed, increasing confusion. 
Redundant taxa: take division Ginkgophyta. It contains a single class, the delightfully named Ginkgoopsida, which contains a single order, Ginkgoales. In the Linnaean hierarchy, each of these taxa contains the next one along, but in terms of monophyly, they are exactly identical to each other, as they share exactly the same most recent ancestor.