酉 (alcohol radical, fermentation) + 每 (every/each, phonetic) = a biological catalyst. The 酉 radical connects to fermentation, where enzymes were first studied.
酉 pictures a wine jar and serves as the fermentation radical. It marks 酶 as a biochemical process — enzymes catalyse fermentation and digestion — and groups with 酒 (wine), 酸 (acid), 酱 (paste), 醉 (drunk).
每 měi gives the sound, shifted to méi. Same phonetic in 梅 (méi, plum), 霉 (méi, mould) and 莓 (méi, berry) — the méi/měi family clusters tightly. Modern Chinese coined 酶 in this style for its biochemistry vocabulary.