[syn: inability, unfitness]
3.  the quality of not being suitable; 
- Example: "the judges agreed on his unfitness for the appointment"
The Collaborative International Dictionary of English v.0.48:
Unfit \Un*fit"\, a. [Pref. un- + fit.]
   Not fit; unsuitable. -- Un*fit"ly, adv. -- Un*fit"ness,
   n.
   [1913 Webster]
WordNet (r) 3.0 (2006):
unfitness
    n 1: poor physical condition; being out of shape or out of
         condition (as from a life of ease and luxury) [syn:
         unfitness, softness] [ant: fitness, physical
         fitness]
    2: lacking the power to perform [syn: inability, unfitness]
       [ant: ability]
    3: the quality of not being suitable; "the judges agreed on his
       unfitness for the appointment" [ant: fitness,
       fittingness]