To be angry. “Dander” is the particles of hair that break off an animal's hair (humans call it “dandruff” when it happens to us). “To get your dander up” calls to mind the hair that stands up on the nape of an enraged dog's neck. Another meaning of the word is the ferment used in making molasses; getting your dander up in that context suggests that your anger is rising the way yeast or any other leavening or fermenting agent does.