The story
Back-formation from syncretic, via a surface analysis by which the pattern of -esis (n) and -etic (adj) is involved, as it is (synchronically validly) with other analogous pairs (e.g., emesis and emetic; diaphoresis and diaphoretic; similarly, catachresis and catachrestic).
Etymology from Wiktionary, CC BY-SA 4.0.