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Phrase(s): get someone’s dander up [and] get someone’s back up; get someone’s hackles up; get someone’s Irish up; put someone’s back up
Fig. to make someone get angry. (Fixed order.) • Now, don’t get your dander up. Calm down. • I insulted him and really got his hackles up. • Bob had his Irish up all day yesterday. I don’t know what was wrong. • Now, now, don’t get your back up. I didn’t mean any harm.
McGrawhill's American Idioms And Phrasal Verbs