ineligibility vs qualification

ineligibility and qualification both are nouns.

Word	Noun	Adjective	Verb	Adverb
ineligibility	Yes	No	No	No
qualification	Yes	No	No	No

As nouns, qualification is a hypernym of ineligibility; that is, qualification is a word with a broader meaning than ineligibility:

ineligibility: the quality or state of being ineligible
qualification: an attribute that must be met or complied with and that fits a person for something

Other hypernyms of ineligibility include making.

ineligibility (noun)	qualification (noun)
the quality or state of being ineligible	the act of modifying or changing the strength of some idea
	an attribute that must be met or complied with and that fits a person for something
	a statement that limits or restricts some claim