failing vs inadequacy

failing and inadequacy both are nouns.

Word	Noun	Adjective	Verb	Adverb
failing	Yes	Yes	No	No
inadequacy	Yes	No	No	No

As nouns, inadequacy is a hyponym of failing; that is, inadequacy is a word with a more specific, narrower meaning than failing:

Other hyponyms of failing include insufficiency, fatigue, flaw.

failing (noun)	inadequacy (noun)
failure to reach a minimum required performance	unsatisfactoriness by virtue of being inadequate
a flaw or weak point	lack of an adequate quantity or number
	a lack of competence

failing (adjective)	inadequacy (adjective)
below acceptable in performance