Untenable
Etymology
From “un-” and “tenable,” from French “tenable,” from Latin “tenere,” to hold. The image is military: a tenable position is one you can hold, an untenable one you cannot defend and must give up. The figurative use keeps that sense of a line that will not hold.
adjective · /un-TEN-uh-buhl/
Impossible to defend, maintain, or hold onto against objection.
What it names
A position that has to be abandoned — not merely weak, but one that cannot be held once it is challenged.
Example
Once the emails surfaced, his claim of ignorance became untenable.
Related idea
An untenable position cannot be held at all; a tenuous one can be held only barely. Untenable is a verdict to abandon; tenuous is a warning that it is fragile.