push back vs offensive

push back and offensive both are nouns.

Word	Noun	Adjective	Verb	Adverb
push back	Yes	No	Yes	No
offensive	Yes	Yes	No	No

As nouns, offensive is a hypernym of push back; that is, offensive is a word with a broader meaning than push back:

Other hypernyms of push back include offence, offense.

push back (noun)	offensive (noun)
the act of forcing the enemy to withdraw	the action of attacking an enemy

push back (adjective)	offensive (adjective)
	unpleasant or disgusting especially to the senses
	causing anger or annoyance
	for the purpose of attack rather than defense
	morally offensive
	violating or tending to violate or offend against
	causing or able to cause nausea

push back (verb)	offensive (verb)
cause to move back by force or influence