To get one’s dander up. ... Dander still means “anger” in the dialectal speech of several English countries, but the full phrase appears to be entirely American. In the dialectal use we find it in Seba Smith’s The Life and Writings of Major Jack Downing, or Downingsville (1830-33), a book dedicated to General Andrew Jackson. In “Letter LXV,” dated July 20, 1833, the Major tells about a quarrel between him and Mr. Van Buren at Concord, in which Van Buren belittles the major’s qualifications for the presidency. “At this,” says the Major, “may dander began to rise ...”

Through the popularity of these humorous yarns and letters, Smith began to have several imitators. The most pretentious was Charles A. Davis, who, in 1834, brought out Letters of J. Downing, Major, Downingville Militia, Second Brigade. In the third “letter,” after describing a dance, in which “Gineral” Jackson participated, the fictitious Downing goes on to say that several of the men, including Van Buren, then tried on Jackson’s coat, after he had retired: “Then cum my turn; but I see how the cat jump’d, ‘so,’ says I, ‘I’ll jest step out and rig in another room:’ and I went strait to the Gineral, and woke him up, and tell’d him all about it -- he was wrathy as thunder -- and when he gets his dander up, it’s no joke, I tell you.”

Hence, to Davis, rather than to Smith, goes the credit, for what it may amount to, for being the first to record this expression. Probably, however, it was a popular phrase of the period, as shortly thereafter it appeared in the works of other writers, among them, Colonel David Crockett in his Life (1835) and upon the lips of “Sam Slick” in Thomas Haliburton’s The Clockmaker (1837-40).

-- from Heavens to Betsy! & Other Curious Sayings, Charles Funk

When a dog or cat is angry or alarmed the hair on its back stands straight up. So too, by analogy, will a person’s. And when he’s thoroughly aroused, according to this humorous phrase, his dandruff will stand up too -- for “dander” is merely “dandruff.”

-- from Dictionary of Word Origins, Jordan Almond