insolence vs offensive activity

insolence and offensive activity both are nouns.

Word	Noun	Adjective	Verb	Adverb
insolence	Yes	No	No	No
offensive activity	Yes	No	No	No

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

insolence: an offensive disrespectful impudent act
offensive activity: a lack of politeness; a failure to show regard for others; wounding the feelings of others

Other hypernyms of insolence include discourtesy, offence, offense.

insolence (noun)	offensive activity (noun)
an offensive disrespectful impudent act	a lack of politeness; a failure to show regard for others; wounding the feelings of others
the trait of being rude and impertinent; inclined to take liberties