insult vs offensive activity

insult and offensive activity both are nouns.

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

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

insult: a deliberately offensive act or something producing the effect of deliberate disrespect
offensive activity: a lack of politeness; a failure to show regard for others; wounding the feelings of others

Other hypernyms of insult include discourtesy, offence, offense.

insult (noun)	offensive activity (noun)
a deliberately offensive act or something producing the effect of deliberate disrespect	a lack of politeness; a failure to show regard for others; wounding the feelings of others
a rude expression intended to offend or hurt

insult (verb)	offensive activity (verb)
treat, mention, or speak to rudely