untenability

adjective

1. incapable of being defended, as an argument, thesis, etc.; indefensible.
2. not fit to be occupied, as an apartment, house, etc.

adjective

1. (of theories, propositions, etc) incapable of being maintained, defended, or vindicated
2. unable to be maintained against attack
3. rare (of a house, etc) unfit for occupation

adj.1640s, “incapable of being held against attack,” from un- (1) “not” + past participle of tenable. Figurative sense is recorded from 1690s.