Tree radical on the left - the indexing radical. Old presses were wooden contraptions: a screw or wedge driving a heavy timber block down onto fruit or seeds. The radical anchors 榨 in the wood-tools family with 槌 (mallet), 桶 (bucket), 杠 (lever), 棒 (rod).
Right side 窄 supplies the sound (zhǎi → zhà with tone shift) and a perfect semantic echo: a press works by squeezing material into a narrower and narrower space. The fit between phonetic and meaning here is unusually tight - every juice extractor is a controlled 'narrowing.'
