offensive vs on the offensive

offensive is a noun but on the offensive is not a noun.

Word	Noun	Adjective	Verb	Adverb
offensive	Yes	Yes	No	No
on the offensive	No	Yes	No	No

offensive (noun)	on the offensive (noun)
the action of attacking an enemy

offensive (adjective)	on the offensive (adjective)
unpleasant or disgusting especially to the senses	actively attacking
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