Why aren't plants and animals capable of assimilating $\ce{N2}$ directly from the atmosphere?
As @Wolfgang Bangerth commented, inertness just means that nitrogen gas doesn't undergo reactions because the NN triple-bond has a very high bond energy and the activation energy for reactions that break the bond (even though thermodynamically favourable) is therefore high. So I suppose that you could say that a major chemical factor in the reactivity of gases is their bond energies.

The key reaction of biological interest for nitrogen is reduction to ammonia, as referenced by the comment of @aretxabaleta. Stryer makes a couple of points that seem chemically relevant (http://www.ncbi.nlm.nih.gov/books/NBK22522/). He says that the reaction pathway for the reduction of nitrogen involves unstable intermediates, and he also mentions that the nitrogenase enzyme in Rhizomium is extremely sensitive to inhibition by oxygen. I am no expert, but I presume that the instability of the intermediates is related to their ease of oxidation. Leguminous plants maintain a very low concentration of free oxygen in their root nodules by synthesising the protein, leghaemoglobin, which mops oxygen up. 

So the answer to the question in the title — why animals (at least) don't fix nitrogen — could well be because as aerobic organisms they would find it very difficult to provide an oxygen-free environment to do this. And the fact that animals can get their metabolizable nitrogen second- or third-hand means that there is no evolutionary pressure to develop such a mechanism. (Most bacteria and plants manage without too.)