In regards to the offender
Do you respect the opinion of person that is abrasive or hurls an insult at you? If not, why let it bother you...his/her opinion should not matter to you. If you do respect that person, stop and consider what they said; is it worthy of your consideration or a reasoned response.
If their comment reveals a personal flaw that you can address, what prevents you from fixing that flaw? (Meditations 8:47) Address the flaw, stop worrying, and get on with your life.
Marcus Aurelius (Meditations 7:26) advises us to examine the offender's understanding of good and evil and if they are contrary to yours (you, being a virtuous person), then it is easier to forgive his transgression, as he is morally confused.
Mastering our emotions helps us build "resilience to" and "tolerance for" other peoples comments and opinions.
Epictetus pointed out that it is not an event that disturbs us, but our judgement of that event - our impression.
In verse 20 of his Handbook, he cautions us to stop giving the OK to your first impression of an event. Take time and think...get control of your emotions.
Self control is essential. Don't let your anger and passion escalate the event, or give the offender any satisfaction. By staying calm, you don't give assent to passions that will upset you.
It is just as true today. Words don't have to hurt...it is our feelings about the words that do us harm. We allow words to hurt us. Centuries later, Shakespeare would use Hamlet to relay a similar message: "There is nothing either good or bad, but thinking makes it so."
Marcus Aurelius tells us (Meditations 8:47) that although it is our own opinion that hurts us, we have the power to change our opinion.
Give yourself time to consider the situation rationally...stay calm. Don't be complicit in hurting your own feelings.
In dealing with mean spirited comments and individuals: respond with wit, or self deprecating humour; or ignore the offense and deny the offender any satisfaction at all.