counterchallenge vs challenge

counterchallenge is not a noun while challenge is a noun.

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

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

counterchallenge (noun)	challenge (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

counterchallenge (verb)	challenge (verb)
challenge in turn	issue a challenge to
	take exception to
	raise a formal objection in a court of law
	ask for identification