Synonyms of 'rudeness'
She is cross at his rudeness.
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He was brusque to the point of discourtesy.
If someone talks or behaves in a rather impolite and disrespectful way, you can call this behaviour impertinence or an impertinence.
The impertinence of the boy is phenomenal!
chutzpah (US , Canadian , informal)
brass neck (British , informal)
Thesaurus for rudeness from the Collins English Thesaurus