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
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