This word has an interesting etymology (and entomology too, come to think of it). It's related to the words piss and ant, but not in the way you might think.

Pismire is an Old English word for "ant," evidently from the Danish "myre," meaning "ant." The "pis" component is thought to come from the fact that many ants secrete formic acid (it's what puts the fire in fire ants, for example). Formic acid, in high concentrations (such as anthills) smells like urine. So, pismire / pissant is a word that means "ant, which by the way smells like piss." One can see why it's an insult that means about the same thing as calling someone an ant, but with an extra edge.

source: The American Heritage® Dictionary of the English Language, Fourth Edition
Available at http://dictionary.com
The origin of the term piss ant/pissant (and the archaic, English country dialect variant, pismire) is to be believed in reference to members of the Formica rufa group which bend their gasters forward and produce a visible stream of formic acid when their nest is disturbed.

Nowadays, since most people are not familiar with F. rufa and relatives (All european species are threatened and have legal protection, and most of the American ones probably ought to also.), the term is used as a general and usually derogatory term for any small ant. In the rural speech of southeastern USA, the belittling "piss ant"/"pissant" contrasts with the respectful (or perhaps fearful is more accurate) expression "bull ant", used for large ants such as Pogonomyrmex badius, Camponotus and even Odontomachus. --Dr. Ant

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