Questions about example sentences with, and the definition and usage of "Offending"

A: I was offended/insulted by her comment about my hair!
She insulted me on purpose! (more intention)
She offended me by being rude. (less intention, maybe an accident)

I was offended by the bad smell. (you can’t be insulted by a smell)
Sexism offends me. (you can’t be insulted by a concept, usually)

My own brother insulted me! >:(
Ha! I insulted her by not bringing her a gift. (mean, maybe you meant to insult her, intention)
I offended her by not bringing her a gift. (more sorrowful, not mean, maybe didn’t mean to offend)

I am going to insult them when I see them. (intention)
They were offended/insulted by my comments.

I don’t want to offend you.
I’m sorry I insulted/offended you.
I didn’t mean to insult/offend you.

Let me know if you have questions! If I wrote a / with both words, it means you can use them interchangeably in that example!