It means to get into a temper. The usage of the word 'dander' may be either a shortening of 'dandruff' or it may derive from 'dander', meaning ferment. It may have been borrowed to form the phrase in order to convey the imagery of an agitated uproar. It might also come from the phrase 'get one's dandruff up', where it followed the imagery of a violent scuffle in which the participant's dandruff might be expected to fly into the air. It was coined in the USA and first appeared in print in 1831.

Übersetzung:

sich ärgern

Gegenteil(e)

The opposite of "to get one's dander up" is "to calm down".

Synonym(e):

You could also say: to become excitedly angry.