Two nits to pick, one major, one minor:

Major:

   "Common names simply don’t work on a large scale. One common name (ie    “cedar”) can refer to 8 different totally unrelated plants, where as Cedrus refers specifically to the genus which contains the species C. libani, C. deodara,  and C. atlantica."

Actually, those 8 different plants are hardly "totally unrelated". They are quite closely related in the evolutionary scheme of things (plants have been around for 1.6 billion years). Red cedar (Juniperus virginiana) and Cedrus (Cedrus atlantica) are both plants, but also Pinidae (conifers), and diverged about 250 Million years ago (time tree.org), so more distantly related that mammals (~80 y), but midway between humans/platypus (200 My) and humans/ducks (320 My). Hardly unrelated.

Minor:

   "Why is it [taxonomy] cool? Because we now group things according to how evolutionarily related are, and how they evolved."

Yes, we group things by how closely related they are, but not necessarily by how distantly related they are in time. Taxonomy is about branch order, not distance in evolutionary time. The same species in a genus may include organisms that diverged several million years ago, but other species may have diverged much more recently. Taxonomy is a kind of evolutionary history that need not have a very regular clock.