"ant," late 14c., pisse-mire (early 14c. as a surname, Henricus pessemere), from pyss "urine" (said to be in reference to the acrid smell of an anthill) + mire "an ant" (mid-13c., early 13c. as a surname), perhaps from an unattested Old English word or from Old Norse maurr "ant" (cognate with Swedish myra, Danish myre, Middle Dutch miere, Dutch mier, Crimean Gothic miera "ant"), from PIE *morwi- (see Formica (2)). Compare pissant, also Old Frisian pis-imme, Norwegian migemaur (first element from Latin mingere); early Dutch mierseycke (with seycke "urine"), Finnish kusiainen (with kusi "urine").
He is as angry as a pissemyre,
Though þat he haue al that he kan desire.
Applied contemptuously to persons from 1560s.
[B]y sun-down [the gals] come pourin out of the woods like pissants out of an old log when tother end's afire. ["Dick Harlan's Tennessee Frolic," in collection "A Quarter Race in Kentucky," Philadelphia, 1846]
word-forming element making adjectives from nouns or verbs, from French -ent and directly from Latin -entem (nominative -ens), present-participle ending of verbs in -ere/-ire. Old French changed it in many words to -ant, but after c. 1500 some of these in English were changed back to what was supposed to be correct Latin. See -ant.