challenge vs repugn

challenge is a noun but repugn is not a noun.

Word	Noun	Adjective	Verb	Adverb
challenge	Yes	No	Yes	No
repugn	No	No	Yes	No

As verbs, repugn is a hypernym of challenge; that is, repugn is a word with a broader meaning than challenge:

Other hypernyms of challenge include contend, contest.

challenge (noun)	repugn (noun)
a call to engage in a contest or fight
questioning a statement and demanding an explanation
a formal objection to the selection of a particular person as a juror
a demand by a sentry for a password or identification
a demanding or stimulating situation

challenge (verb)	repugn (verb)
issue a challenge to	to make the subject of dispute, contention, or litigation
take exception to
raise a formal objection in a court of law
ask for identification