The longer answer (which you know I’m itching to provide) is circuitous. Of unknown origin (Webster’s and the Oxford English Dictionaries agree on this), it can be confused with another dudgeon, which means “a type of wood [assumed to be boxwood] used to make the handles of daggers,” and hence “a dagger-handle made of such wood” and “a dagger” itself. This dudgeon is found most famously in Macbeth’s hallucinated knife: “Come, let me clutch thee / I have thee not, and yet I see thee still; / And on thy blade and dudgeon gouts of blood." First found in English in the early fifteenth century, dudgeon is a borrowing from Anglo-French, although the ultimate origin is unknown.
There is no obvious connection between the “anger” word and the “hilt-wood” word, but it might conceivably refer to someone grabbing a dagger in anger.
But the etymology grows even murkier. In 1573, Gabriel Harvey in his Letter-book, wrote, “... in marvelous great duggin,” meaning “indignation.” One suggestion is that this word comes from the Italian aduggiare ("to overshadow”), relating it to umbrage. Another possible root is the Welsh word dygen, meaning "malice or resentment," but as the O.E.D. heartbrokenly laments, “There is a distressing lack of evidence for that theory.”
The Bard of Buffalo Bayou, whose normal state of mind is one of extremely high dudgeon, snarled the following lines before vanishing in a wisp of acrid smoke:
Hell, yes, I’m in high dudgeon,
With no plans to rise above it.
I’m a certified curmudgeon—
You wanna make something of it?