ineligibility vs making

ineligibility and making both are nouns.

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

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

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

Other hypernyms of ineligibility include qualification.

ineligibility (noun)	making (noun)
the quality or state of being ineligible	the act that results in something coming to be
	(usually plural) the components needed for making or doing something
	an attribute that must be met or complied with and that fits a person for something