Using 'curt' may imply rudeness or impatience, often it's unintended. Her curt 'I'm busy' sounded abrupt, even though she didn't mean to be rude.
Pro Tip 2/3
Response to Rudeness
'Curt' can be a reaction to disrespect, signaling the end of a conversation. After the insult, his curt 'goodbye' showed he wouldn't tolerate rudeness.
Pro Tip 3/3
Cultural Variations
In some cultures, being 'curt' can be viewed more negatively than in others. His curt manner was accepted at home but seen as unfriendly abroad.