"Please forgive me Sage but in my eyes Duryodhana is not an insulting name but rather most suitable for someone who is from the Boon of Lord Shiva."
Karna also folded his hands out of respect for the Sage but with same as before without fear in his tone answered Durvasa.
Karna is already given the reason why the name Duryodhana is not an insult but rather an honour to be called by this name. It's just a matter of perspective on how one wants to take it.
The only problem is now that to get the chance to convince Durvasa, Karna looked at the enraged face of Durvasa knowing that it would not be an easy task to do it.
At this point he really wanted dear Mama (Uncle) to take the wheel as he is the most suitable to handle this situation, There is no one better manipul-*Ahem* convincing man available in the Aryavart.