Wiktionary
untenability
n. The condition of being untenable
Usage examples of "untenability".
Like the Newtonian mechanics of an earlier age, they were just approximations that would be repealed with the development of more precise theoretical models and improved measurement techniques, similar to the way in which careful experiments with light waves had demonstrated the untenability of classical physics and resulted in the formulation of special relativity.
There are numerous excellent discussions of the untenability of natural selection as the primary mechanism of evolution.